Differentiation under the integral sign:

Leibnitz's Rule

If g is continuous on [a, b] and f₁ (x) and f₂ (x) are differentiable functions the values of which lie in [a , b], then 

Illustration: If f(x) = cos x -  then  show that f'' (x) + f (x) = - cos x                              

Solution:               

Illustration: If a function f(x) can be defined ∀ x ∈ R such that , a ∈ R⁺ exist. If g(x) = . Prove that 

Solution:            

                              Diffrentiate w.r.t. x

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