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#