Question

find the first partial derivative:

f(x, y) = y^5 -3xy

could you please explain how to do these as well?

Answer 1

with respect to x or y ?

Answer 2

the first one lol

Answer 3

partials are just like usual except the none interested in variable is considered a constant

Answer 4

Well, there's two partial derivatives, one with respect to x and one with respect to y. To find the partial derivative with respect to x you differentiate with respect to x while holding y constant, giving:
\[\frac{\partial f}{\partial x} = -3y\]
Similarly,
\[\frac{\partial f}{\partial y} = 5y^4-3x\]

Answer 5

x y^2 with respect to x is: y^2

x y^2 with respect to y is: 2x y

Answer 6

okay thanks!