Calculus • Step-by-Step

Derivative of x² with Steps

Find the derivative of x² step-by-step using the power rule. See the exact formula, power subtraction, and final solution f'(x) = 2x.

Problem Statement

\frac{d}{dx}[x^2]

Final Result

f'(x) = 2 \cdot x

Formula Required: Power Rule for Differentiation

Multiply by the existing power n and subtract 1 from the exponent.

\frac{d}{dx}[x^n] = n \cdot x^{n-1}

2 Steps

Set up the differentiation problem with respect to variable $x$.

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

Apply the Power Rule to compute the derivative.

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

Interactive Calculator

Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.

The derivative of x² is 2x. Using the power rule d/dx[x^n] = n·x^(n-1), multiply by 2 and reduce the power to 2 - 1 = 1.

Substitute x = 3 into f'(x) = 2x: f'(3) = 2(3) = 6. The slope of the tangent line at x = 3 is 6.