Question

If $y = e^{(1 + \log_e \, x)}$, then $\frac{dy}{dx}$ is equal to :

• A. e
• B. 1
• C. 0
• D. $\log_e \, x . x$

Answer 1

Answer: (A)

e

Answer 2

We have, $y = e^{(1 + \log_e \, x)}$ $\Rightarrow \:\: y = e^1 \times e^{\log x}$ $\Rightarrow \:\:\: y = ex \:\:\: [\because \:\: e^{\log} e^x = x]$ On differentiating, w. r. to x we get $\frac{dy}{dx} = \frac{d}{dx} (ex)$ $\Rightarrow \:\:\: \frac{dy}{dx} = e$