Question

The differential Coefficient of ƒ(log_e x) w.r.t x, where

ƒ(x) = log_e x is –

• A. x/log_e x
• B. log_e x/x
• C. (x log_e x)^–1
• D. None

Answer 1

Answer: (C)

(x log_e x)^–1

Answer 2

Let u = ƒ(log_e x)

\ $\frac{du}{dx}$ = ƒ¢ (log_e x) . $\frac{1}{x}$ … (1)

given ƒ(x) = log_e x

\ Ģ(x) = $\frac{1}{x}$

\ ƒ¢(log_e x) = $\frac{1}{\log_{e}x}$ … (2)

From (1) and (2),

$\frac{du}{dx}$ = $\frac{1}{x\log_{e}x}$

= (x log_e x)^–1.