Question

If $y=f\left(x^2+2\right)$ 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)

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