Method of DifferentiationeasyFree

Method of Differentiation: Equals

JEE Maths question with a full step-by-step solution.

Question
If f(x)=log⁡xf(x)=\log x, then f′(log⁡x)f'(\log x) equals
Axlog⁡x\dfrac{x}{\log x}
Blog⁡xx\dfrac{\log x}{x}
C1xlog⁡x\dfrac{1}{x\log x}
D1log⁡x\dfrac{1}{\log x}correct
Solution
Step 1: f(x)=log⁡x  ⇒  f′(x)=1xf(x)=\log x\;\Rightarrow\;f'(x)=\dfrac{1}{x}. Step 2: Substitute x↦log⁡xx\mapsto\log x into f′f':
f′(log⁡x)=1log⁡xf'(\log x)=\dfrac{1}{\log x}
 Correct answer: (4)
Still stuck on this question?Ask your doubt on WhatsApp
Similar questions
Method of Differentiation · easy
If f′(x)=3x2+6f'(x) = \sqrt{3x^2+6} and y=f(x3)y = f(x^3), then at x=1x = 1, (dydx)\left(\dfrac{dy}{dx}\right) is equal to.
Method of Differentiation · easy
If yy is a function of xx and log⁡(x+y)=2xy\log(x+y) = 2xy, then y′(0)y'(0) is.
Method of Differentiation · easy
ddx[sin⁡x+cos⁡x1+sin⁡2x]\dfrac{d}{dx}\left[\dfrac{\sin x + \cos x}{\sqrt{1 + \sin 2x}}\right], where 0<x<π40 < x < \dfrac{\pi}{4}, is:
Method of Differentiation · easy
If y=1+x2+x41+x+x2y=\dfrac{1+x^{2}+x^{4}}{1+x+x^{2}} and dydx=ax+b\dfrac{dy}{dx}=ax+b, then the values of aa and bb are

Solve more, learn faster

Sign up free to solve more JEE Maths questions and explore doMath — timed drills, mastery sprints, bookmarks, and chapter-wise progress tracking.

Sign up freeExplore doMath