Question

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

• A. 5
• B. 25
• C. 15
• D. 20
• E. 10

Answer 1

Answer: (E)

10

Given, $y=f(x^2+2)$
On differentiating both sides w.r.t. $x$, we get
$\frac{dy}{dx}=f^{\prime }(x^2+2)\times 2x$
Put $x=1$, we get
$\frac{dy}{dx}=f^{\prime }(1^2+2)\times 2=f^{\prime }\left(3\right)\times 2$
$=5\times 2$ $[\because f^{\prime }(3)=5]$ given
$=10$