Question

the partial derivative of f(x,y)=x+xy with respect tp y is

Answer 1

Answer:

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Answer 2

Using the chain rule with u = xy for the partial derivatives of cos(xy) ∂ ∂x cos(xy) = ∂ cos(u) ∂u ∂u ∂x = − sin(u)y = −y sin(xy) , ∂ ∂y cos(xy) = ∂ cos(u) ∂u ∂u ∂y = − sin(u)x = −x sin(xy) . Thus the partial derivatives of z = sin(x) cos(xy) are ∂z ∂x = cos(xy) cos(x) − y sin(x) sin(xy) , ∂z ∂y = −x sin(x) sin(xy)

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