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Partial Derivative – A quotient of functions inside arcsin function – Exercise 3294

Exercise 

Find partial derivatives of the function

z(x,y)=\arcsin\frac{x}{\sqrt{x^2+y^2}}

Final Answer

z'_x (x,y)=\frac{|y|}{x^2+y^2}

z'_y (x,y)=\frac{-xy}{|y|(x^2+y^2)}

Solution

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