Answer to Question #143349 in Calculus for Moel Tariburu

Question #143349
Find the partial derivative ∂z/∂x and ∂z/∂y of the function x^4y^3+8x^2y
1
Expert's answer
2020-11-10T20:01:35-0500

Let us find the partial derivatives of the function


z=x4y3+8x2yz=x^4y^3+8x^2y :


zx=x4xy3+8x2xy=4x3y3+16xy\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


zy=x4y3y+8x2yy=3x4y2+8x2\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



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