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Solution assignment 08 Partial differentiation

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Assignment 8

Calculate the first derivatives of the following function.

f(x,y)=xe^{xy^2}

Solution

f_x=1\cdot{e^{xy^2}}+x[e^{xy^2}]_x=e^{xy^2}+xy^2e^{xy^2}=e^{xy^2}(1+xy^2)

We applied the product and the chain rule.

f_y=x\cdot2xy\cdot{e^{xy^2}}=2x^2ye^{xy^2}

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