The differential coefficient of log10 x with respect to logx 10 is

Question

The differential coefficient of log10 x with respect to logx 10 is (A) 1 (B) -(log10 x)2 (C) (logx 10)2 (D) (x2/100)

Tardigrade Admin · Accepted Answer

Let, u=log10 x and v=logx 10 ⇒ u=(loge x/loge â¡ 1 0) and v=(loge 1 0/loge â¡ x) Now, (d u/d x)=(1/x loge 1 0) and (d v/d x)=(log)e 10[(- 1/x ((log)e â¡ x)2)] ∴ (d u/d v)=(d u / d x/d v / d x)=(1/x (log)e 10)÷(- (log)e â¡ 1 0/x ((log)e â¡ x)2) =(- ((log)e x)2/((log)e â¡ 10)2)=-(((log)e â¡ x/(log)e â¡ 10))2 =-((log)10 x)2

Q. The differential coefficient of $l o g_{10} x$ with respect to $l o g_{x} 10$ is

$1$

$- (l o g_{10} x)^{2}$

$(l o g_{x} 10)^{2}$

$\frac{x ^{2}}{100}$

Q. The differential coefficient of log10​x with respect to logx​10 is

1

−(log10​x)2

(logx​10)2

100x2​

Q. The differential coefficient of $l o g_{10} x$ with respect to $l o g_{x} 10$ is

$1$

$- (l o g_{10} x)^{2}$

$(l o g_{x} 10)^{2}$

$\frac{x ^{2}}{100}$