How do you find the derivative of z=x(y^2)-e^(xy)z=x(y2)−exy?
1 Answer
Feb 27, 2017
(partial z) / (partial x) = y^2-ye^(xy) ∂z∂x=y2−yexy
(partial z) / (partial y) = 2xy-xe^(xy) ∂z∂y=2xy−xexy
Explanation:
We have:
z=xy^2-e^(xy)z=xy2−exy
Which is a function of two variables, so the derivatives are;
(partial z) / (partial x) = y^2-ye^(xy) ∂z∂x=y2−yexy
(partial z) / (partial y) = 2xy-xe^(xy) ∂z∂y=2xy−xexy
Remember when partially differentiating: differentiate with respect to the variable in question, treating the other variables as constant.
