Derivative of $x^{5}$

The derivative of x^5 is 5 x^4.

The derivative of $x^{5}$ is $5 x^{4}$ .

f(x) =

\frac{d}{dx}\left[x^{5}\right] = 5 x^{4}

Type any function of x; the derivative is computed symbolically in your browser.

\frac{d}{dx}\left[x^{5}\right] = 5 x^{4}

Graph of f(x) = x^5 and its derivative. The dashed line is the tangent at x = 1; its slope is f'(1) = 5.

How to work it out

1
We differentiate $f(x) = x^{5}$ with respect to x. The rule that applies is the standard derivative.
$f(x) = x^{5}$
2
This is a standard derivative from the table.
3
Simplify:
$f'(x) = 5 x^{4}$
4
Differentiating once more gives the second derivative, which tells you about curvature:
$f''(x) = 20 x^{3}$

LaTeX source of the formulas on this page

\[ \frac{d}{dx}\left[x^{5}\right] = 5 x^{4} \]
\[ f(x) = x^{5} \]
\[ f'(x) = 5 x^{4} \]
\[ f''(x) = 20 x^{3} \]

What is the derivative of

x^{5}

The derivative of $x^{5}$ is $5 x^{4}$ .

What is the second derivative of

x^{5}

20 * $x^{3}$ .

Which rule do you use for

x^{5}

The standard derivative.

What is the slope of

x^{5}

at x = 1?