Answer
(a) $f(x) = sin(x+sin~2x)$
We can use the graph of $f(x)$ to make a sketch of $f'(x)$
(b) $f'(x) = cos(x+sin~2x)~(1+2~cos~2x)$
Work Step by Step
(a) $f(x) = sin(x+sin~2x)$
We can use the graph of $f(x)$ to make a sketch of $f'(x)$
Note that $f'(x)$ has negative values when the slope of $f(x)$ has a negative slope, $f'(x)$ is 0 when the slope of $f(x)$ is 0, and $f'(x)$ has positive values when the slope of $f(x)$ has a positive slope.
(b) $f'(x) = cos(x+sin~2x)\cdot \frac{d}{dx}(x+sin~2x)$
$f'(x) = (1+2~cos~2x)\cdot cos(x+sin~2x)$
We can use a graphing calculator to graph $f'(x)$ and compare it to our sketch in part (a)
