frac{d}{dx} left{ log left( frac{e^x}{1 + e^x | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $y = \log \left( \frac{e^x}{1 + e^x} \right)$.Using the property of logarithms,$\log \left( \frac{a}{b} \right) = \log a - \log b$,we get:$y =

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) Let $y = \log \left( \frac{e^x}{1 + e^x} \right)$.Using the property of logarithms,$\log \left( \frac{a}{b} \right) = \log a - \log b$,we get:$y = \log(e^x) - \log(1 + e^x) = x - \log(1 + e^x)$.Now,differentiate with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx}(x) - \frac{d}{dx}(\log(1 + e^x))$.$\frac{dy}{dx} = 1 - \frac{1}{1 + e^x} \cdot \frac{d}{dx}(1 + e^x)$.$\frac{dy}{dx} = 1 - \frac{e^x}{1 + e^x}$.$\frac{dy}{dx} = \frac{1 + e^x - e^x}{1 + e^x} = \frac{1}{1 + e^x}$.Since $\frac{1}{1 + e^x}$ is not among the given options,the correct answer is $(D)$.

$\frac{d}{dx} \left\{ \log \left( \frac{e^x}{1 + e^x} \right) \right\} = $

Similar Questions

Differentiate the following with respect to $x$: $\log (\log x)$,where $x > 1$.

Find the derivative: $\frac{d}{dx} \log (\sqrt{x - a} + \sqrt{x - b})$

The differential coefficient of $f[\log (x)]$ with respect to $x$ when $f(x) = \log x$ is:

$\frac{d}{dx} \left[ \log \sqrt{\sin \sqrt{e^x}} \right] = $

If $y = \log \left( \frac{1 + \sqrt{x}}{1 - \sqrt{x}} \right)$,then $\frac{dy}{dx} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module