Calculus • Step-by-Step

Derivative of (2x + 1)³ with Steps

Step-by-step differentiation of (2x + 1)³ using the general power rule (chain rule) to get 6(2x + 1)².

Problem Statement

\frac{d}{dx}[(2x + 1)^3]

Final Result

f'(x) = 6 \cdot \left(2 \cdot x+1\right)^{2}

Formula Required: General Power Rule (Chain Rule)

Bring down the power, reduce the power by 1, and multiply by the derivative of the inside.

\frac{d}{dx}[(g(x))^n] = n(g(x))^{n-1} \cdot g'(x)

2 Steps

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

\frac{d}{dx} \left[ \left(2 \cdot x+1\right)^{3} \right]

Apply the Power Rule to compute the derivative.

\frac{d}{dx} \left[ \left(2 \cdot x+1\right)^{3} \right] = 6 \cdot \left(2 \cdot x+1\right)^{2}

Interactive Calculator

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

Use the chain rule: 3(2x+1)² · d/dx[2x+1] = 3(2x+1)² · 2 = 6(2x+1)².