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What is a derivative?What is an integral?Derivative rulesIntegration rulesThe power rule

Derivative of x²

ddx[x2]=2x\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.

Derivation

  1. Power rule

    d/dx[xⁿ] = n·xⁿ⁻¹.

    ddx[x2]=2x\frac{d}{dx}\left[x^{2}\right] = 2 x
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  • f(x) = x²
  • f′(x)

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

Open in the derivative calculator

Questions students ask

What is the derivative of x²?

ddx[x2]=2x\frac{d}{dx}\left[x^{2}\right] = 2 x.

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.