If $f$ Is a Function Of $x$ And $y$ , And $y$ Is a Function Of

Essay

If $f$ is a function of $x$ and $y$ , and $y$ is a function of $x$ , then indirectly $f$ depends only on $x : g ( x ) = f ( x , y ( x ) )$ . If $f ( x , y ) = \sin x + \sqrt { 1 - y ^ { 2 } }$ and $y ( x ) = \cos x$ , calculate $\frac { d g } { d x }$ .