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

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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 $ . . . . . . $.

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