Problems related to differentiation under the integral sign are very common in IIT-JEE. We will see how to solve such problems using Leibniz's Rule given below.
Problem 1
If f(x) is differentiable and ,
find f(4/25)
(IIT-JEE 2004)
Solution
Differentiating both sides,
Hence, f(4/25)=2/5 for t=2/5
PS: Note that -2/5 is also a valid answer. It was not among the options for the MCQ.
Problem 2
Solve
This is in 0/0 form. So we can apply L'Hospital's Rule directly. Differentiating the numerator and the denominator separately, we have,
Problem 1
If f(x) is differentiable and ,
(IIT-JEE 2004)
Solution
Differentiating both sides,
PS: Note that -2/5 is also a valid answer. It was not among the options for the MCQ.
Problem 2
Solve
(IIT-JEE 2007)
Solution This is in 0/0 form. So we can apply L'Hospital's Rule directly. Differentiating the numerator and the denominator separately, we have,
