EasyDerivativesCalculus

Find $\frac{d}{dx}\left(x^3\right)$ .

A direct application of the power rule.

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Final answer

f'(x) = 3{x}^{2}

How we read your problem

Find the derivative of x³ with respect to x.

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

Step-by-step solution

Power rule: d/dx[xⁿ] = n·xⁿ⁻¹
$\frac{d}{dx}\left[{x}^{3}\right] = 3{x}^{2}$
Combine and simplify
$f'(x) = 3{x}^{2}$

Formulas used

Power rule
$\frac{d}{dx}x^n = n x^{n-1}$

The derivative is built from the outside in: sums split into terms, constants factor out, products and quotients use their rules, and every composite function multiplies by the derivative of its inside (chain rule).

Verification

Cross-checked numerically against an independent symbolic differentiator at 8 sample points ✓

About derivatives

Power, product, quotient and chain rules.

Power rule

Bring the exponent down and reduce it by one.

\frac{d}{dx}x^n = nx^{n-1}

Chain rule

Differentiate the outer function, then multiply by the derivative of the inner.

\frac{d}{dx}f(g(x)) = f'(g(x))\,g'(x)

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Medium

Find the derivative of