Derivatives

Differentiate products, quotients and chains like x³·sin(x) or sin(x²) with the rule named, every piece shown and the result simplified.

All derivative problems

$\frac{d}{dx}\left[x^{2}\right]$
$\frac{d}{dx}\left[x^{3}\right]$
$\frac{d}{dx}\left[x^{4}\right]$
$\frac{d}{dx}\left[x^{5}\right]$
$\frac{d}{dx}\left[\sqrt{x}\right]$
$\frac{d}{dx}\left[\frac{1}{x}\right]$
$\frac{d}{dx}\left[\sin\left(x\right)\right]$
$\frac{d}{dx}\left[\cos\left(x\right)\right]$
$\frac{d}{dx}\left[\tan\left(x\right)\right]$
$\frac{d}{dx}\left[e^{x}\right]$
$\frac{d}{dx}\left[\ln\left(x\right)\right]$
$\frac{d}{dx}\left[\arctan\left(x\right)\right]$
$\frac{d}{dx}\left[x^{2} x^{3}\right]$
$\frac{d}{dx}\left[x^{2} x^{4}\right]$
$\frac{d}{dx}\left[x^{2} x^{5}\right]$
$\frac{d}{dx}\left[x^{2} \sqrt{x}\right]$
$\frac{d}{dx}\left[x^{2} \frac{1}{x}\right]$
$\frac{d}{dx}\left[x^{2} \sin\left(x\right)\right]$
$\frac{d}{dx}\left[x^{2} \cos\left(x\right)\right]$
$\frac{d}{dx}\left[x^{2} \tan\left(x\right)\right]$
$\frac{d}{dx}\left[x^{2} e^{x}\right]$
$\frac{d}{dx}\left[x^{2} \ln\left(x\right)\right]$
$\frac{d}{dx}\left[x^{2} \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[x^{3} x^{4}\right]$
$\frac{d}{dx}\left[x^{3} x^{5}\right]$
$\frac{d}{dx}\left[x^{3} \sqrt{x}\right]$
$\frac{d}{dx}\left[x^{3} \frac{1}{x}\right]$
$\frac{d}{dx}\left[x^{3} \sin\left(x\right)\right]$
$\frac{d}{dx}\left[x^{3} \cos\left(x\right)\right]$
$\frac{d}{dx}\left[x^{3} \tan\left(x\right)\right]$
$\frac{d}{dx}\left[x^{3} e^{x}\right]$
$\frac{d}{dx}\left[x^{3} \ln\left(x\right)\right]$
$\frac{d}{dx}\left[x^{3} \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[x^{4} x^{5}\right]$
$\frac{d}{dx}\left[x^{4} \sqrt{x}\right]$
$\frac{d}{dx}\left[x^{4} \frac{1}{x}\right]$
$\frac{d}{dx}\left[x^{4} \sin\left(x\right)\right]$
$\frac{d}{dx}\left[x^{4} \cos\left(x\right)\right]$
$\frac{d}{dx}\left[x^{4} \tan\left(x\right)\right]$
$\frac{d}{dx}\left[x^{4} e^{x}\right]$
$\frac{d}{dx}\left[x^{4} \ln\left(x\right)\right]$
$\frac{d}{dx}\left[x^{4} \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[x^{5} \sqrt{x}\right]$
$\frac{d}{dx}\left[x^{5} \frac{1}{x}\right]$
$\frac{d}{dx}\left[x^{5} \sin\left(x\right)\right]$
$\frac{d}{dx}\left[x^{5} \cos\left(x\right)\right]$
$\frac{d}{dx}\left[x^{5} \tan\left(x\right)\right]$
$\frac{d}{dx}\left[x^{5} e^{x}\right]$
$\frac{d}{dx}\left[x^{5} \ln\left(x\right)\right]$
$\frac{d}{dx}\left[x^{5} \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[\sqrt{x} \frac{1}{x}\right]$
$\frac{d}{dx}\left[\sqrt{x} \sin\left(x\right)\right]$
$\frac{d}{dx}\left[\sqrt{x} \cos\left(x\right)\right]$
$\frac{d}{dx}\left[\sqrt{x} \tan\left(x\right)\right]$
$\frac{d}{dx}\left[\sqrt{x} e^{x}\right]$
$\frac{d}{dx}\left[\sqrt{x} \ln\left(x\right)\right]$
$\frac{d}{dx}\left[\sqrt{x} \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[\frac{1}{x} \sin\left(x\right)\right]$
$\frac{d}{dx}\left[\frac{1}{x} \cos\left(x\right)\right]$
$\frac{d}{dx}\left[\frac{1}{x} \tan\left(x\right)\right]$
$\frac{d}{dx}\left[\frac{1}{x} e^{x}\right]$
$\frac{d}{dx}\left[\frac{1}{x} \ln\left(x\right)\right]$
$\frac{d}{dx}\left[\frac{1}{x} \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[\sin\left(x\right) \cos\left(x\right)\right]$
$\frac{d}{dx}\left[\sin\left(x\right) \tan\left(x\right)\right]$
$\frac{d}{dx}\left[\sin\left(x\right) e^{x}\right]$
$\frac{d}{dx}\left[\sin\left(x\right) \ln\left(x\right)\right]$
$\frac{d}{dx}\left[\sin\left(x\right) \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[\cos\left(x\right) \tan\left(x\right)\right]$
$\frac{d}{dx}\left[\cos\left(x\right) e^{x}\right]$
$\frac{d}{dx}\left[\cos\left(x\right) \ln\left(x\right)\right]$
$\frac{d}{dx}\left[\cos\left(x\right) \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[\tan\left(x\right) e^{x}\right]$
$\frac{d}{dx}\left[\tan\left(x\right) \ln\left(x\right)\right]$
$\frac{d}{dx}\left[\tan\left(x\right) \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[e^{x} \ln\left(x\right)\right]$
$\frac{d}{dx}\left[e^{x} \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[\ln\left(x\right) \arctan\left(x\right)\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{2}}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{3}}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{4}}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{x^{5}}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\sqrt{x}}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\frac{1}{x}}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\sin\left(x\right)}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\cos\left(x\right)}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\tan\left(x\right)}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{e^{x}}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{\ln\left(x\right)}{\arctan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{x^{2}}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{x^{3}}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{x^{4}}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{x^{5}}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{\sqrt{x}}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{\frac{1}{x}}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{\sin\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{\cos\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{\tan\left(x\right)}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{e^{x}}\right]$
$\frac{d}{dx}\left[\frac{\arctan\left(x\right)}{\ln\left(x\right)}\right]$
$\frac{d}{dx}\left[\sin\left(x^{2}\right)\right]$
$\frac{d}{dx}\left[\sin\left(2 x\right)\right]$
$\frac{d}{dx}\left[\sin\left(3 x\right)\right]$
$\frac{d}{dx}\left[\sin\left(5 x\right)\right]$
$\frac{d}{dx}\left[\sin\left(x^{3}\right)\right]$
$\frac{d}{dx}\left[\sin\left(x^{2} + 1\right)\right]$
$\frac{d}{dx}\left[\sin\left(1 - x\right)\right]$
$\frac{d}{dx}\left[\sin\left(-x\right)\right]$
$\frac{d}{dx}\left[\cos\left(x^{2}\right)\right]$
$\frac{d}{dx}\left[\cos\left(2 x\right)\right]$
$\frac{d}{dx}\left[\cos\left(3 x\right)\right]$
$\frac{d}{dx}\left[\cos\left(5 x\right)\right]$
$\frac{d}{dx}\left[\cos\left(x^{3}\right)\right]$
$\frac{d}{dx}\left[\cos\left(x^{2} + 1\right)\right]$
$\frac{d}{dx}\left[\cos\left(1 - x\right)\right]$
$\frac{d}{dx}\left[\cos\left(-x\right)\right]$
$\frac{d}{dx}\left[\tan\left(x^{2}\right)\right]$
$\frac{d}{dx}\left[\tan\left(2 x\right)\right]$
$\frac{d}{dx}\left[\tan\left(3 x\right)\right]$
$\frac{d}{dx}\left[\tan\left(5 x\right)\right]$
$\frac{d}{dx}\left[\tan\left(x^{3}\right)\right]$
$\frac{d}{dx}\left[\tan\left(x^{2} + 1\right)\right]$
$\frac{d}{dx}\left[\tan\left(1 - x\right)\right]$
$\frac{d}{dx}\left[\tan\left(-x\right)\right]$
$\frac{d}{dx}\left[e^{x^{2}}\right]$
$\frac{d}{dx}\left[e^{2 x}\right]$
$\frac{d}{dx}\left[e^{3 x}\right]$
$\frac{d}{dx}\left[e^{5 x}\right]$
$\frac{d}{dx}\left[e^{x^{3}}\right]$
$\frac{d}{dx}\left[e^{x^{2} + 1}\right]$
$\frac{d}{dx}\left[e^{1 - x}\right]$
$\frac{d}{dx}\left[e^{-x}\right]$
$\frac{d}{dx}\left[\ln\left(x^{2}\right)\right]$
$\frac{d}{dx}\left[\ln\left(2 x\right)\right]$
$\frac{d}{dx}\left[\ln\left(3 x\right)\right]$
$\frac{d}{dx}\left[\ln\left(5 x\right)\right]$
$\frac{d}{dx}\left[\ln\left(x^{3}\right)\right]$
$\frac{d}{dx}\left[\ln\left(x^{2} + 1\right)\right]$
$\frac{d}{dx}\left[\ln\left(1 - x\right)\right]$
$\frac{d}{dx}\left[\ln\left(-x\right)\right]$
$\frac{d}{dx}\left[\sqrt{x^{2}}\right]$
$\frac{d}{dx}\left[\sqrt{2 x}\right]$
$\frac{d}{dx}\left[\sqrt{3 x}\right]$
$\frac{d}{dx}\left[\sqrt{5 x}\right]$
$\frac{d}{dx}\left[\sqrt{x^{3}}\right]$
$\frac{d}{dx}\left[\sqrt{x^{2} + 1}\right]$
$\frac{d}{dx}\left[\sqrt{1 - x}\right]$
$\frac{d}{dx}\left[\sqrt{-x}\right]$