Question

solve for d/dx by implicit differentiation: (e^y)(cosx)=1+sin(xy)

Answer 1

what have you attempted? or what do you not understand about it?

Answer 2

f g = 1 + h

f' g + f g' = h'

Answer 3

so far i have (e^y)(y')(-sinx)=0+sin(xy) and im not sure if this is right or how to find the derivative of sin(xy)

Answer 4

(e^y)' (cosx) + (e^y) (cosx)'

y' e^y cosx - e^y sinx

for the left side

Answer 5

sin(xy) is a chain rule; h(k) to h'(k) k'

Answer 6

sin(xy) to cos(xy) * (xy)'
cos(xy) * (y+xy')