If y = f(x^2 + 2) and f'(3) = 5,then frac{dy} | vedclass

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(D) Given the function $y = f(x^2 + 2)$.Applying the chain rule to differentiate with respect to $x$,we get:$\frac{dy}{dx} = f'(x^2 + 2) \cdot \frac{d

Vedclass · Accepted Answer

$10$

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(D) Given the function $y = f(x^2 + 2)$.Applying the chain rule to differentiate with respect to $x$,we get:$\frac{dy}{dx} = f'(x^2 + 2) \cdot \frac{d}{dx}(x^2 + 2)$$\frac{dy}{dx} = f'(x^2 + 2) \cdot (2x)$Now,evaluate the derivative at $x = 1$:$\left. \frac{dy}{dx} \right|_{x=1} = f'(1^2 + 2) \cdot (2 \cdot 1)$$\left. \frac{dy}{dx} \right|_{x=1} = f'(3) \cdot 2$Given that $f'(3) = 5$,substitute this value into the expression:$\left. \frac{dy}{dx} \right|_{x=1} = 5 \cdot 2 = 10$

If $y = f(x^2 + 2)$ and $f'(3) = 5$,then $\frac{dy}{dx}$ at $x = 1$ is:

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