Please help me understand the following step in arriving at the answer to this question:

$$x \sin (\pi*x) = \int\limits_{0}^{x^2} f(t) dt, find f(4);$$

The answer has this step:
differentiate both sides and get:
\sin (\pi*x) + \pi*x*\cos(\pi*x) = 2*x*f(x^2)\]
How did the upper limit become 2x here from chainrule?

Question

Please help me understand the following step in arriving at the answer to this question:

$$x \sin (\pi*x) = \int\limits_{0}^{x^2} f(t) dt, find f(4);$$

The answer has this step:
differentiate both sides and get:
\sin (\pi*x) + \pi*x*\cos(\pi*x) = 2*x*f(x^2)\]
How did the upper limit become 2x here from chainrule?

kenshin · Answer

$$\sin (\pi*x) + \pi*x*\cos(\pi*x) = 2xf(x^2) this is the step i'm \not getting, where did the 2xf(x^2) come from, the answer said \it was from chainrule and FTC1$$