Differentiate.

1. $\frac{d}{dx}(\sin(x−5))$

   Hint (a):

   $\sin(x−5)$ is a horizontal shift of $\sin x$. The slopes will shift with the points.

   Answer (a):

   $\cos(x−5)$

2. $\frac{d}{dx}(x^{82}−6)$

   Hint (b):

   Use the Power Rule.

3. $\frac { d } { d m } ( - 2 m ^ { 3 / 2 } )$

   Hint (c):

   Use the Power Rule.

4. $\frac{d}{dx}(x+6)^3$

   Hint (d):

   You could expand first or... refer to the hint in part (a).