Question

If $y=e^{x^2}$, then what is $\frac{dy}{dx}$ at $x=\pi$ equal to?

• A. $(1+\pi )e^{{\pi }^2}$
• B. $2\pi e^{{\pi }^2}$
• C. $2e^{{\pi }^2}$
• D. $e^{{\pi }^2}$

Answer 1

Answer: (B)

$2\pi e^{{\pi }^2}$

We have $y=e^{x^2}$

Differentiate with respect to $x$, we get

$\frac{dy}{dx}=e^{x^2}\cdot 2x$

At $x=\pi$ we get

${\frac{dy}{dx}}_{(x=\pi )}=e^{{\pi }^2}\cdot 2\pi =2\pi e^{{\pi }^2}$