Derivative of x²

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

Differentiate again: \frac{d^2}{dx^2}\left[x^{2}\right] = 2.

Plug into the derivative: f'(1) = 2. That is the slope of the tangent line there; drag the graph to see it.

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

A direct use of the power rule: bring the 2 down and lower the exponent by one. The slope of the parabola doubles as x doubles.

Drag the graph · at x = 1.20 the slope is 2.4, the height of the dashed curve.

Questions students ask

What is the derivative of x²?

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

What is the second derivative of x²?

Differentiate again: $\frac{d^2}{dx^2}\left[x^{2}\right] = 2$ .

What is the slope of x² at x = 1?

Plug into the derivative: $f'(1) = 2$ . That is the slope of the tangent line there; drag the graph to see it.

How do you find the derivative of x²?

A direct use of the power rule: bring the 2 down and lower the exponent by one. The slope of the parabola doubles as x doubles.

What is the integral of x²?

Use the integral calculator to find the antiderivative of x² step by step.