Question

Given: z=z(x,y)
find...
dz/dy partial if:
x^4+3xy^2+5z=sin(z)

Answer 1

can u explain?

Answer 2

make it equal to 0 and differentiate with respect to y?

Answer 3

just derivate implicitly. Think of x^4+3xy^2+5z=sin(z) like
F(x,y,z) = x^4+3xy^2+5z-sin(z)=0
where z=z(x,y)
sry, i errased the 1º answer, don't know what happened...

Answer 4

so if z is a function of x and y how do i differentiate lets say -5z or -sin(z)?

Answer 5

and no worries, i want to be able to get to answer myself

Answer 6

-5z is -5z(x,y) so just use chain rule

Answer 7

ohhhh ok i see, than this is easy, thanks

Answer 8

wait distribute or treat them seperatly?

Answer 9

still confused haha

Answer 10

\[[-5z]'_{y} = -5*z'_{y}*dy\]
chain rule...