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 $x$ : $g ( x ) = f ( x , y ( x ) )$ . Use the Chain Rule to write an expression for $\frac { d g } { d x }$ in terms of $\frac { \delta f } { \delta x }$ and $\frac { \delta f } { \delta y }$ .