Question
The differential coefficient of $$f\left( {{{\log }_e}\,x} \right)$$ with respect to $$x,$$ where $$f\left( x \right) = {\log _e}\,x,$$ is :
A.
$$\frac{x}{{{{\log }_e}\,x}}$$
B.
$$\frac{1}{x}{\log _e}\,x$$
C.
$$\frac{1}{{x{{\log }_e}\,x}}$$
D.
none of these
Answer :
$$\frac{1}{{x{{\log }_e}\,x}}$$
Solution :
$$\eqalign{
& f\left( {{{\log }_e}\,x} \right) = {\log _e}\left( {{{\log }_e}\,x} \right) \cr
& \therefore \,\frac{{df\left( {{{\log }_e}\,x} \right)}}{{dx}} = \frac{1}{{{{\log }_e}\,x}}.\frac{1}{x} \cr} $$