Question

let f(x,y)=x^2y+y^2z. use chain rule to calculate df/ds, where x = s+t, y = st, z = 2s-t.

the answer if got is
df/ds=2xy+x^2t+2yzt+2y^2s
i am working out a test review and need to know if thats right!
let f(x,y)=x^2y+y^2z. use chain rule to calculate df/ds, where x = s+t, y = st, z = 2s-t.

the answer if got is
df/ds=2xy+x^2t+2yzt+2y^2s
i am working out a test review and need to know if thats right!
@Mathematics

Answer 1

\[{\partial f \over \partial s}={\partial f \over \partial x}{\partial x \over \partial s}+{\partial f \over \partial y}{\partial y \over \partial s}+{\partial f \over \partial z}{\partial z \over \partial s}=2xy(1)+(x^2+2yz)(t)+y^2(2).\]
Simplifying yields to \(\frac{\partial f}{\partial s}=2xy+x^2t+2yzt+2y^2.\)

Answer 2

The only difference from your answer is that you have an s in your last term. This is wrong unless you made a mistake in your question regarding \(z\).

Answer 3

ok yeah i messed up dz/ds = 2s instead of just 2, which is why i had the extra s at the end.

Answer 4

but thanks again AnwaraA!
by the way, how do you make the partial derivative symbol, are you using another program to type equations?

Answer 5

No. You can use the "Equation" button below and write "partial". Call me Anwar!

Answer 6

oh ok thats pretty cool. thanks again Anwar!:)

Answer 7

You're welcome! :)