Derivative of $x^{2}$

The derivative of $x^{2}$ is $2 x$ .

f(x) =

\frac{d}{dx}\left[x^{2}\right] = 2 x

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

\frac{d}{dx}\left[x^{2}\right] = 2 x

Graph of f(x) = x^2 and its derivative. The dashed line is the tangent at x = 1; its slope is f'(1) = 2.

How to work it out

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

LaTeX source of the formulas on this page

\[ \frac{d}{dx}\left[x^{2}\right] = 2 x \]
\[ f(x) = x^{2} \]
\[ f'(x) = 2 x \]
\[ f''(x) = 2 \]

What is the derivative of

x^{2}

The derivative of $x^{2}$ is $2 x$ .

What is the second derivative of

x^{2}

Which rule do you use for

x^{2}

The standard derivative.

What is the slope of

x^{2}

at x = 1?