Derivative of `x^3`

Step-by-step differentiation

Answer

\frac{d}{d x} [x^{3}]

3 \cdot x^{2}

Step-by-step solution

1Power Rule
$\frac{d}{d x} [x^{3}] = 3 \cdot x^{3 - 1}$
The exponent is $3$ . Bring it down in front as a coefficient, then reduce the power by $1$ .
✓Final Answer
$\frac{d}{d x} [x^{3}] = 3 \cdot x^{2}$
The first derivative simplifies to $3 \cdot x^{2}$ .

Understanding this derivative

Differentiating x³ is a single-rule problem: everything follows from the power rule. That makes it a good expression for isolating and practicing that one technique.

The power rule is the workhorse step: bring the exponent down as a coefficient and reduce the exponent by one.

A good way to verify a derivative by hand is to compare it against the step-by-step breakdown above — each step names the rule being applied, so you can pinpoint exactly where your own work diverges if the answers differ.

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Derivative of x^3

Step-by-step solution

Understanding this derivative

Derivative of `x^3`