# Math Help - Derivating integrals

1. ## Derivating integrals

Hi !

This is just curiosity.. : I'd like to know how you'd do it and what you're going to say. I don't need the result.

$C(x)=\int_0^\infty e^{-t} \cos(xt) \ \frac{dt}{\sqrt{t}}$

$S(x)=\int_0^\infty e^{-t} \sin(xt) \ \frac{dt}{\sqrt{t}}$

Establish the equation :

$C'(x)=-x \cdot S'(x)-\frac 12 \cdot S(x)$

2. Yes, sort of

But I wanted to know if you guys know another way to do it.
I have one. So I want to see how things are taught elsewhere ^^