Question

Find the partial derivative ∂z/∂x and ∂z/∂y of the function x^4y^3+8x^2y

Answer 1

Let us find the partial derivatives of the function

$z=x^4y^3+8x^2y$ :

$\frac{\partial z}{\partial x}= \frac{\partial x^4}{\partial x}y^3+8\frac{\partial x^2}{\partial x}y=4x^3y^3+16xy$

$\frac{\partial z}{\partial y}= x^4\frac{\partial y^3}{\partial y}+8x^2\frac{\partial y}{\partial y}=3x^4y^2+8x^2$