Partial Derivatives of f(x,y,z): Solve Confusing Homework

[sarahaha288]

Homework Statement

I need to find the partial derivitives of f(x,y,z)=50-14x+3y^2-2xy (e^z)

Homework Equations

The Attempt at a Solution

i think the x-partial would be -14+2ye^z+2xye^z... but I'm not sure and I'm confused of how to find the others!

 

[rock.freak667]

f(x,y,z)=50-14x+3y²-2xye^z

simply when taking the partial derivative w.r.t. to a variable, you treat the rest as constants.

so for ∂f/∂x, we would treat y and z as constants and differentiate normally.

∂f/∂x=∂/∂x(50)-∂/∂x(14x)+∂/∂x(3y²)-∂/∂x(2xye^z)


How did you get your answer though?


So for ∂f/∂z, treat x and y as constants. It is similar for ∂f/∂y.