Home > CALC > Chapter 7 > Lesson 7.3.4 > Problem7-151

7-151.

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

1. $1 +\operatorname{cos}(xy)$

1. $1 + y\operatorname{cos}(xy​)$

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.

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