# Please answer the question attached in it. Its a bit complicated to write. It is from integral calculus.

2081 Points
4 years ago
obviously, f(3)=0
now we use leibniz formula for differentiation under the integral sign and obtain
f’(x)= 1/sqrt(x^4+3x^2+13)
now, since g is inverse if f,
g(f(x))=x
differentiate both sides
g’(f(x))*f’(x)=1
in above eqn, put x=3
g’(f(3))*f’(3)=1
g’(0)*f’(3)=1
or g’(0)=1/f’(3)
now f’(3)= 1/sqrt(3^4+3*3^2+13)
=1/sqrt(121)
=1/11
so, g’(0)= 11