Can you solve differentiation

June 3, 2026Mathematics

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Answer

6x(x^2 + 1)^2

6 steps

To differentiate $y = (x^2 + 1)^3$ , we will use the chain rule.

Identify the outer and inner functions.
Let the outer function be $f(u) = u^3$ and the inner function be $u = g(x) = x^2 + 1$ .
Differentiate the outer function with respect to $u$ .
$\frac{df}{du} = \frac{d}{du}(u^3) = 3u^2$
Differentiate the inner function with respect to $x$ .
$\frac{du}{dx} = \frac{d}{dx}(x^2 + 1) = 2x$
Apply the chain rule, which states $\frac{dy}{dx} = \frac{df}{du} \cdot \frac{du}{dx}$ .
Substitute the expressions from Step 2 and Step 3:
$\frac{dy}{dx} = (3u^2)(2x)$
Substitute back $u = x^2 + 1$ into the expression.
$\frac{dy}{dx} = 3(x^2 + 1)^2 (2x)$
Simplify the expression.
$\frac{dy}{dx} = 6x(x^2 + 1)^2$
The final answer is $6x(x^2 + 1)^2$ .

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