Derivative of $x^{3}$

The derivative of x^3 is 3 x^2.

The derivative of $x^{3}$ is $3 x^{2}$ .

f(x) =

\frac{d}{dx}\left[x^{3}\right] = 3 x^{2}

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

\frac{d}{dx}\left[x^{3}\right] = 3 x^{2}

Graph of f(x) = x^3 and its derivative. The dashed line is the tangent at x = 1; its slope is f'(1) = 3.

How to work it out

1
We differentiate $f(x) = x^{3}$ with respect to x. The rule that applies is the standard derivative.
$f(x) = x^{3}$
2
This is a standard derivative from the table.
3
Simplify:
$f'(x) = 3 x^{2}$
4
Differentiating once more gives the second derivative, which tells you about curvature:
$f''(x) = 6 x$

LaTeX source of the formulas on this page

\[ \frac{d}{dx}\left[x^{3}\right] = 3 x^{2} \]
\[ f(x) = x^{3} \]
\[ f'(x) = 3 x^{2} \]
\[ f''(x) = 6 x \]

What is the derivative of

x^{3}

The derivative of $x^{3}$ is $3 x^{2}$ .

What is the second derivative of

x^{3}

6x.

Which rule do you use for

x^{3}

The standard derivative.

What is the slope of

x^{3}

at x = 1?