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  • Find the derivative of  <img alt="u=x^{5}" src="https://entrancecorner.oncodecogs.

Find the derivative of  u=x^{5}  with respect to v=5logx

Option: 1

u


Option: 2

v


Option: 3

uv


Option: 4

u^{2}v


Answers (1)

best_answer

Let u=x^5, v=5 \log x Now differentiate " u " with respect to " x" \begin{aligned} & \frac{\mathrm{d}(\log u)}{\mathrm{d} x}=\frac{\mathrm{d}(5 \log x)}{\mathrm{d} x} \\ & \frac{1}{u} \frac{\mathrm{d} u}{\mathrm{~d} x}=5 \frac{1}{x} \\ & \frac{\mathrm{d} u}{\mathrm{~d} x}=5\left(\frac{u}{x}\right) \end{aligned}

Similarly differentiate “v” with respect to “x”

 

\begin{aligned} & \frac{\mathrm{d} v}{\mathrm{~d} x}=5\left(\frac{1}{x}\right) \\ & \frac{\mathrm{d} u}{\mathrm{~d} v}=\frac{\frac{\mathrm{d} u}{\mathrm{~d} x}}{\frac{\mathrm{d} v}{\mathrm{~d} x}}=\frac{5\left(\frac{u}{x}\right)}{5\left(\frac{1}{x}\right)}=u \end{aligned}

Posted by

Kuldeep Maurya

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