The derivative of log _{e^2}(log x) with resp | vedclass

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

Question

(B) Let $y = \log _{e^2}(\log x)$.Using the logarithmic property $\log _{b^n} a = \frac{1}{n} \log _b a$,we can rewrite the expression as:$y = \frac{1

Vedclass · Accepted Answer

$\frac{1}{2x \log x}$

Vedclass · Answer

(B) Let $y = \log _{e^2}(\log x)$.Using the logarithmic property $\log _{b^n} a = \frac{1}{n} \log _b a$,we can rewrite the expression as:$y = \frac{1}{2} \log _e(\log x)$Now,differentiating with respect to $x$:$\frac{dy}{dx} = \frac{d}{dx} \left[ \frac{1}{2} \log _e(\log x) \right]$$\frac{dy}{dx} = \frac{1}{2} \cdot \frac{1}{\log x} \cdot \frac{d}{dx}(\log x)$$\frac{dy}{dx} = \frac{1}{2} \cdot \frac{1}{\log x} \cdot \frac{1}{x}$$\frac{dy}{dx} = \frac{1}{2x \log x}$Thus,the correct option is $B$.

The derivative of $\log _{e^2}(\log x)$ with respect to $x$ is $ . . . . . . $.

Similar Questions

The value of $\log _{e} 2 \cdot \frac{d}{dx}(\log _{\cos x} \operatorname{cosec} x)$ at $x=\frac{\pi}{4}$ is.

If $f(x)=\log _{x^{2}}\left(\log _{e} x\right)$,then $f^{\prime}(x)$ at $x=e$ is

$\frac{d}{dx}(\log \tan x) = $

If $y = \log_2(\log_2(x))$,then $\frac{dy}{dx}$ is equal to

If $y=\log_{\sin x} \tan x$,then $\left(\frac{dy}{dx}\right)_{x=\frac{\pi}{4}}$ has the value

Vedclass Test Series

Exam Paper Generator

Online Exam Module