The differential coefficient of f( log x) w.r.t x, where f(x)= log x is:

Question

The differential coefficient of f( log x) w.r.t x, where f(x)= log x is: (A)  (x/ log x)  (B)  ( log x/x)  (C)  (x log x)-1  (D) none of these

Tardigrade Admin · Accepted Answer

We have, f(x)= log x ⇒ f( log x)= log log x On differentiating w.r.t. x on both sides, we get f'( log x) (1/x)=(1/ log x) ⋅ (1/x) ⇒ f( log x)=(1/ log x)

Q. The differential coefficient of $f (lo g x)$ w.r.t $x,$ where $f (x) = lo g x$ is:

$\frac{x}{l o g x}$

$\frac{l o g x}{x}$

$(x lo g x)^{- 1}$

none of these

We have, $f (x) = lo g x$
$\Rightarrow f (lo g x) = lo g lo g x$
On differentiating w.r.t. $x$ on both sides, we get
$f^{'} (lo g x) \frac{1}{x} = \frac{1}{l o g x} \cdot \frac{1}{x}$
$\Rightarrow f (lo g x) = \frac{1}{l o g x}$

Q. The differential coefficient of f(logx) w.r.t x, where f(x)=logx is:

logxx​

xlogx​

(xlogx)−1