Question

The value of differentiation of $e^{x^2}$ with respect to$e^{2x–1}$ at $x=1$ is

• A. $e$
• B. $0$
• C. $e^{-1}$
• D. $1$

Answer 1

The correct option is D

$1$

Explanation for the correct option:

Find the required value.

Let$u=e^{x^2}$

On differentiating w.r.t. $x$, we get

$\frac{du}{dx}=e^{x^2}2x$

Let $v=e^{2x–1}$

On differentiating w.r.t. $x$, we get

$\frac{dv}{dx}=2e^{2x–1}$

$\therefore \frac{du}{dv}=\frac{{\displaystyle \left(\frac{du}{dx}\right)}}{{\displaystyle \left(\frac{{\displaystyle dv}}{{\displaystyle dx}}\right)}}$

$$\begin{gathered} =\frac{e^{x^2}2x}{2e^{2x–1}} \\ =x{e}^{x^2-2x+1} \end{gathered}$$

Now, ${\left(\frac{du}{dv}\right)}_{\left(x=1\right)}=1\times e^{1-2+1}$

$=1$

Hence, option (D) is the correct answer.