CPM Homework Help : CALC3RD Problem 7-198

If $y = x + \sin(xy)$ , then $\frac { d y } { d x }=$

$\frac { 1 + y \operatorname { cos } ( x y ) } { 1 - x \operatorname { cos } ( x y ) }$

Hint:

Implicit differentiation with the Chain Rule can be messy.

Steps:

$\frac{d}{dx}y=\frac{d}{dx}(x+\text{sin}(xy))$

$y'=1+\text{cos}(xy)\left ( y\frac{dx}{dx}+x\frac{dy}{dx} \right )$

$\text{Solve for }\frac{dy}{dx}.$