0

Guest

Courses New

Letf(x)=x^x,x belongs to (0,∞) and letg(x) be inverse of f(x) ,then g’(x) must be

Letf(x)=x^x,x belongs to (0,∞) and letg(x) be inverse of f(x) ,then g’(x) must be
 

Question Image
Grade:12

1 Answers

Aditya Gupta
2081 Points
4 years ago
we know that f(g(x))= x
diff both sides using chain rule
f’(g(x))*g’(x)=1
or g’(x)= 1/f’(g(x))
now f’(x)= x^x(1+lnx)= f(x)*(1+lnx)
so f’(g(x))= f(g(x))*(1+lng(x)), but f(g(x))= x
so f’(g(x))= x(1+lng(x))
so that g’(x)= 1/f’(g(x))= 1/x(1+lng(x))
option c is correct.
kindly approve please :)

Think You Can Provide A Better Answer ?

Other Related Questions on Differential Calculus

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More