### Home > CALC3RD > Chapter Ch7 > Lesson 7.4.2 > Problem7-198

7-198.

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

1. $1 + \cos(xy)$

1. $1 + y\cos(xy)$

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

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

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

Implicit differentiation with the Chain Rule can be messy.

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

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

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