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Partial Derivative – A sum of ln function and an exponential function – Exercise 3247

Exercise 

Find the partial derivatives of the function

z(x,y)=\ln (x+y^2)+5^{xy^2}

Final Answer

z'_x (x,y)=\frac{1}{x+y^2}+y^2 \ln 5\cdot5^{xy^2}

z'_y (x,y)=\frac{2y}{x+y^2}+2xy\ln 5\cdot5^{xy^2}

Solution

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