What is the derivative of x³ + 2x?

June 7, 2026Mathematics

ScanSolve AI Answer

Answer

The derivative of $x^3 + 2x$ is $3x^2 + 2$ .

3 steps

Steps:
To find the derivative of $f(x) = x^3 + 2x$ , we apply the sum rule and the power rule for differentiation.

Derivative of $x^3$
Using the power rule, $\frac{d}{dx}(x^n) = nx^{n-1}$ .
$\frac{d}{dx}(x^3) = 3x^{3-1} = 3x^2$ .
Derivative of $2x$
Using the constant multiple rule and the power rule.
$\frac{d}{dx}(2x) = 2 \cdot \frac{d}{dx}(x^1) = 2 \cdot 1x^{1-1} = 2 \cdot 1x^0 = 2 \cdot 1 = 2$ .
Sum Rule
The derivative of a sum of functions is the sum of their derivatives.
$\frac{d}{dx}(x^3 + 2x) = \frac{d}{dx}(x^3) + \frac{d}{dx}(2x)$
$\frac{d}{dx}(x^3 + 2x) = 3x^2 + 2$ .

Was this helpful?

A new problem that tests the same skill.

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question