# How do you implicitly differentiate #9=-y/x+xsiny#?

##### 1 Answer

Apr 23, 2017

#### Explanation:

differentiate

#color(blue)"implicitly with respect to x"#

#"differentiate " y/x" using the "color(blue)"quotient rule"#

#"differentiate " xsiny" using the "color(blue)"product rule"#

#rArr0=-((xdy/dx-y)/(x^2))+xcosy.dy/dx+siny#

#rArr(xdy/dx-y)/x^2=xcosy.dy/dx+siny#

.

#rArrxdy/dx-y=x^3cosy.dy/dx+x^2siny#

#rArrxdy/dx-x^3cosydy/dx=x^2siny+y#

#rArrdy/dx(x-x^3cosy)=x^2siny+y#