Finding the integral

Question

Let F(x) = ∫e^{u^2} + cos(u) du   with upper limit = 7x, lowerlimit = 0

Compute F'(0)

 

I have no idea how to approach this question the 7x in the upper limit is quite off putting

Answer 1

According to the Fundamental Theorem of Calculus F'(x)= e^(7x)^cos (7x)d/dx(7x)

 

7[(e^(7x) +cos (7x)]

 

So F'(0)= 7*(e^0+cos(0))= 7*2= 14

Answer 2

 

F(x) = ∫^7x ₀ e^{u^2} + cos(u) du

F'(x)=?

 

In general,

F(x)= ∫^x _a f(u) du

F'(x)= f(x)  (the upper limit is inputted into the integral with derivatives of integrals)