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Q.

The derivative of $\log_{10} x$ with respect to $x^{2}$ is

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a

$\frac{1}{2 x^{2} \log 10}$

b

$\frac{1}{2 x \log 10}$

c

$\frac{- 1}{2 x \log 10}$

d

$\frac{- 1}{2 x^{2} \log 10}$

answer is B.

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Detailed Solution

Let $y = \log_{10} x \Rightarrow y = \frac{\log x}{\log 10} \Rightarrow \frac{d y}{d x} = \frac{1}{\log 10} \times \frac{1}{x}$

$u = x^{2} \Rightarrow \frac{d u}{d x} = 2 x$

$\frac{d y}{d u} = \frac{1}{2 x^{2} \log 10}$

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