Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Differentiate each of the following w.r.t. x log [log (log x5)]

Differentiate each of the following w.r.t. x
\log [\log (\log x^5)]

Answers (1)

Differentiate the given function w.r.t x

Let Assume y=\log [\log (\log x^5)]

y= log [log (log x\textsuperscript{5})]

Let log(log x\textsuperscript{5}) = u

Let Assume log x\textsuperscript{5}=v

Let Assume x\textsuperscript{5}=w

Differentiate both side w.r.t x

\\ \frac{\mathrm{dy}}{\mathrm{du}}=\frac{\mathrm{d}}{\mathrm{du}}[\log \mathrm{u}] \\ \frac{\mathrm{dy}}{\mathrm{du}}=\frac{1}{\mathrm{u}} \\ \frac{\mathrm{d} \mathrm{w}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{d} \mathrm{x}}\left(\mathrm{x}^{5}\right) \\ \frac{\mathrm{d} \mathrm{w}}{\mathrm{dx}}=5 \mathrm{x}^ 4 \\ \frac{\mathrm{d} \mathrm{v}}{\mathrm{d} \mathrm{w}}=\frac{\mathrm{d}}{\mathrm{d} \mathrm{x}}(\log \mathrm{w}) \\ \frac{\mathrm{d} \mathrm{v}}{\mathrm{dw}}=\frac{1}{\mathrm{w}} \frac{\mathrm{d}}{\mathrm{d} \mathrm{x}}(\mathrm{w})

Now, Bu using chain rule we get, Differentiation of \log [\log (\log x^5)]

\begin{aligned} &\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{dy}}{\mathrm{du}} \times \frac{\mathrm{du}}{\mathrm{dv}} \times \frac{\mathrm{d} \mathrm{v}}{\mathrm{dw}} \times \frac{\mathrm{d} \mathrm{w}}{\mathrm{dx}}\\ &\frac{d y}{d x}=\frac{1}{u} \times \frac{1}{v} \times \frac{1}{w} \times 5 x^{4}\\ &\text { Now, Substitute the value of } u_{\ell} v \text { and } w \text { then, we get }\\ &\frac{d y}{d x}=\frac{1}{\log \left(\log x^{5}\right)} \times \frac{1}{\log x^{5}} \times \frac{1}{x^{5}} \times 5 x^{4}\\ &=\frac{5}{x \cdot \log \left(\log x^{5}\right) \log x^{5}} \end{aligned}

Hence, This the differentiation of given function.      

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question