Question

Use implicit differentiation to find the derivative of the family of curves
sin(xy)+x5+y5=c.

dy/dx=?

I got
(-5x^4-ycos(xy))/(xcos(xy)+5y^4)). what am I doing wrong? Help please

Answer 1

sin(xy)+x^5+y^5=c
cos(xy)(y+xy') + 5x^4 + 5y^4 y' = 0
y*cos(xy) + x*cos(xy)y' + 5x^4 + 5y^4 y' = 0

(x*cos(xy) + 5y^4)y' = -(y*cos(xy) + 5x^4)

y' =
   y*cos(xy) + 5x^4
- -------------------------
   x*cos(xy) + 5y^4