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Partial Derivative – A function to the power of a function – Exercise 3250

Exercise 

Find the partial derivatives of the function

z(x,y)={(1+xy)}^y

Final Answer

z'_x (x,y)=y^2{(1+xy)}^{y-1}

z'_y (x,y)={(1+xy)}^y(\ln (1+xy)+\frac{xy}{1+xy})

Solution

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