Chapter 3 - Section 3.6 - Derivatives of Logarithmic Functions - 3.6 Exercises - Page 224: 41

$f(x) = sin~x+ln~x$ $f'(x) = cos~x+\frac{1}{x}$ We can see a sketch of the graphs below.

$f(x) = sin~x+ln~x$ $f'(x) = cos~x+\frac{1}{x}$ $f'(x)$ seems reasonable since $f'(x)$ 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.