Answer
$y'=3+10\pi^2 x\sin{(\pi x)}^2.$
Work Step by Step
$y=f(x)+g(x)\rightarrow f(x)=3x$; $g(x)=-5\cos{(\pi x)}^2$
Using Power Rule: $f'(x)=3$
Using Chain Rule:
$u=(\pi x)^2$; $\dfrac{du}{dx}=2\pi^2x$
$g(u)=-5\cos{u};\dfrac{d}{du}g(u)=5\sin{u}$
$\dfrac{d}{dx}g(x)=\dfrac{d}{du}g(u)\times\dfrac{du}{dx}=10\pi^2 x\sin{(\pi x)}^2.$
$y'=f'(x)+g'(x)=3+10\pi^2 x\sin{(\pi x)}^2.$
