If f(x)=sin-1x+cos-1x find f '(x) and sketch the graph of y=f(x)
If f(x) = cos-1(sinx) find f '(x) and sketch the graph of y=f(x) for -pi<or equalto x< or equal to pi
In fact (can you see why?), so the graph is a horizontal line at for
2 Note that , for all valid values of , and . The derivative takes negative values since decreases from to as increases from to .
Thus, using the Chain Rule, if while is increasing in the range .
Now increases from to as increases from to , so in this range . But for decreases from to , and for decreases from to . Hence in these ranges is increasing, and therefore .
The graph is as shown in the attached diagram.