Key to "Find both first partial derivatives. z=x2e2y"

allhvasstH

Answered question

2021-04-11

Find both first partial derivatives.

z = x^{2} e^{2 y}

Answer & Explanation

averes8

Skilled2021-04-13Added 92 answers

Step 1
Given function is

z = x^{2} e^{2 y}

.
Partial derivative means derivative of function with respect to one variables keeping other variables as constant.
Finding partial derivative of the function with respect to x keeping y as constant.

\frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (x^{2} e^{2 y})

= e^{2 y} \cdot \frac{\partial}{\partial x} (x^{2})

= e^{2 y} \cdot 2 x

= 2 x_{e}^{2 y}

Therefore,

\frac{\partial z}{\partial x} = 2 x_{e}^{2 y}

.
Step 2
Now, finding partial derivative with respect to y keeping other variable as constant.

\frac{\partial z}{\partial y} = \frac{\partial}{\partial y} (x^{2} e^{2 y})

= x^{2} \cdot 2 e^{2 y}

= 2 x^{2} e^{2 y}

Hence,

\frac{\partial z}{\partial x} = 2 x e^{2 y} and \frac{\partial z}{\partial y} = 2 x e^{2 y}

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Find both first partial derivatives. z = x^{2}e^{2y}

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Answer & Explanation

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