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Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability1 Mark
Question
Differentiation of $\log \left[\log \left(\log x^5\right)\right] \text{w.r.t.} \ x$ is :
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Answer

$(D)$ Suppose $y=\log \left[\log \left(\log x^5\right)\right]$
$\therefore \frac{d y}{d x} =\frac{1}{\log \left(\log x^5\right)} \cdot \frac{d}{d x}\left[\log \left(\log x^5\right)\right]$
$ =\frac{1}{\log \left(\log x^5\right)} \cdot \frac{1}{\log x^5} \frac{d}{d x}\left(\log x^5\right)$
$=\frac{1}{\log \left(\log x^5\right)} \cdot \frac{1}{\log x^5} \cdot \frac{1}{x^5} \cdot \frac{d}{d x}\left(x^5\right)$
$=\frac{1}{\log \left(\log x^5\right)} \cdot \frac{1}{\log x^5} \cdot \frac{1}{x^5} \cdot 5 x^4$
$=\frac{5}{x\left(\log x^5\right) \log \left(\log x^5\right)}$

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