## allyfranken find the first partial derivative: f(x, y) = y^5 -3xy could you please explain how to do these as well? 2 years ago 2 years ago

1. TuringTest

with respect to x or y ?

2. amistre64

the first one lol

3. amistre64

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

4. dave444

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, $\frac{\partial f}{\partial y} = 5y^4-3x$

5. amistre64

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

6. allyfranken

okay thanks!