Derivative of log x w.r.t 1x is

Let u=log⁡x and v=1x, thendudx=1x and dvdx=−1x2.∴ dudv=dudxdvdx=1x−1x2=−x∴ Option (c) is the correct answer.

Derivative of log x w.r.t 1x is

Let u=log⁡x and v=1x, thendudx=1x and dvdx=−1x2.∴ dudv=dudxdvdx=1x−1x2=−x∴ Option (c) is the correct answer.

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Derivative of log x w.r.t $\frac{1}{x}$ is

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$- \frac{1}{x^{3}}$

$- \frac{1}{x}$

$- x$

$\frac{1}{x}$

answer is C.

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Detailed Solution

Let $u = \log x$ and $v = \frac{1}{x}$ , then

$\frac{d u}{d x} = \frac{1}{x}$ and $\frac{d v}{d x} = - \frac{1}{x^{2}}$ .

$∴ \frac{d u}{d v} = \frac{\frac{d u}{d x}}{\frac{d v}{d x}} = \frac{\frac{1}{x}}{- \frac{1}{x^{2}}} = - x$

$∴$ Option (c) is the correct answer.

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Derivative of log x w.r.t $\frac{1}{x}$ is