Question

Find d/dx (sin y+y cos x) where y = g(x).

Answer 1

okk
d(siny)/dx+d(ycosx)/dx
=cosy*dy/dx+y*(-sinx)+cosx*dy/dx
as y=g(x)...so dy/dx=dg(x)/dx=g'(x)
=cosy*g'(x)-sinx*y+cosx*g'(x)

Answer 2

ok so -sinx*y .... yhis has y so dont we change this to g'(x)

Answer 3

anyone?

Answer 4

why g'(x)?

Answer 5

dy/dx is g'(x)
y is g(x)

Answer 6

why didnt we change y to g(x)

Answer 7

because it is troublesome to do it before you differentiate it. you will get the same result, but much harder

Answer 8

you should substitute it after you differentiate it

Answer 9

so whats the final answer ? one given by g17

Answer 10

given by me