## University Calculus: Early Transcendentals (3rd Edition)

At $x=2$, $y'=-5$.
We have $y=f(g(x))$, $f'(3)=-1$, $g'(2)=5$ and $g(2)=3$. According to the Chain Rule: $$y'=(f(g(x)))'=f'(g(x))\times g'(x)$$ At $x=2$: $$y'(2)=f'(g(2))\times g'(2)$$ We have $g(2)=3$ and $g'(2)=5$: $$y'(2)=f'(3)\times5$$ Finally, we have $f'(3)=-1$: $$y'(2)=-1\times5=-5$$