The differential coefficient of f[ (x)] when f(x) = x is - Vidyadip

MCQ

The differential coefficient of $f[\log (x)]$ when $f(x) = \log x$ is

A
$x\log x$
B
${x \over {\log x}}$
✓
${1 \over {x\log x}}$
D
${{\log x} \over x}$

✓

Answer

Correct option: C.

${1 \over {x\log x}}$

c
(c) $\because f(x)=\log x$ ;

$\therefore f[\log x] = \log \log x$

$f'[\log x] = \frac{1}{{\log x}}.\frac{d}{{dx}}\log x = \frac{1}{{x\log x}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The general solution of the $D E\ x^2 \frac{d y}{d x}=x^2+x y+y^2$ is

The order and degree of the differential equation $\frac{{{d^2}y}}{{d{x^2}}} = \sqrt {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} $ is

The function $\text{f}(\text{x})=\cot^{-1}\text{x}+\text{x}$ increases in the interval:

Choose the correct answer from given four options in each of the Exercise $:$ If $A$ and $B$ are invertible matrices, then which of the following is not correct?

Principal value of $\tan ^{-1}(-1)$ :

The solution set of the constraints $x+2 y \geq 11,3 x+4 y \leq 30,2 x+5 y \leq 30, x \geq 0, y \geq 0$ includes the point.

The direction cosines of a line equally inclined to three mutually perpendicular lines having direction cosines as ${l_1},{m_1},{n_1};{l_2},{m_2},{n_2}$ and ${l_3},{m_3},{n_3}$ are

The differential coefficient of ${a^x} + \log x.\sin x$ is

The value of the determinant $\begin{vmatrix}\text{a}^2&\text{a}&1\\\cos\text{nx}&\cos(\text{n}+1)\text{x}&\cos(\text{n}+2)\text{x}\\\sin\text{nx}&\sin(\text{n}+1)\text{x}&\sin(\text{n}+2)\text{x}\end{vmatrix}$ is independent of:

If the points $P$ and $Q$ are respectively the circumcentre and the orthocentre of a $\triangle ABC$, then $\overrightarrow{ PA }+\overrightarrow{ PB }+\overrightarrow{ PC }$ is equal to