The derivative of log x with respect to 1x is ______. - Mathematics

Question

The derivative of log x with respect to $\frac{1}{x}$ is ______.

Options

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

MCQ

Fill in the Blanks

Solution

The derivative of log x with respect to $\frac{1}{x}$ is – x.

Explanation:

Let u = log x

and v = $\frac{1}{x}$

Differentiate w.r. to ‘x’

$\frac{d u}{d x} = \frac{1}{x}$

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

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

$\Rightarrow \frac{d u}{d v}$ = – x

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Logarithmic Differentiation

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