## Calculus (3rd Edition)

$$\frac{d^3}{dx^3}(9-x)^8 = -336( 9-x)^5.$$
We have $$\frac{d}{dx}(9-x)^8=8( 9-x)^7(-1)=-8( 9-x)^7$$ and $$\frac{d^2}{dx^2}(9-x)^8 =-56( 9-x)^6(-1)=56( 9-x)^6.$$ Hence, $$\frac{d^3}{dx^3}(9-x)^8 = 56\frac{d}{dx}(( 9-x)^6\\ =336( 9-x)^5 (-1)=-336( 9-x)^5.$$