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Question: Differential coefficient of log<sub>10</sub> x w.r.t. log<sub>x</sub>10 is–...

Differential coefficient of log10 x w.r.t. logx10 is–

A

–(log⁡10)2(log⁡x)2\frac{(\log 10)^{2}}{(\log x)^{2}}

B

(log⁡x10)2(log⁡10)2\frac{(\log_{x}10)^{2}}{(\log 10)^{2}}

C

(log⁡10x)2(log⁡10)2\frac{(\log_{10}x)^{2}}{(\log 10)^{2}}

D

–(log⁡x)2(log⁡10)2\frac{(\log x)^{2}}{(\log 10)^{2}}

Answer

–(log⁡x)2(log⁡10)2\frac{(\log x)^{2}}{(\log 10)^{2}}

Explanation

Solution

y = log10x z = logx10 = 1log⁡10x\frac{1}{\log_{10}x}

y = 1z\frac{1}{z} ⇒ dydz\frac{dy}{dz} = – 1z2\frac{1}{z^{2}} = –1(log⁡x10)2\frac{1}{(\log_{x}10)^{2}} = –(log⁡x)2(log⁡10)2\frac{(\log x)^{2}}{(\log 10)^{2}}