"Find both first partial derivatives. z=exy" was answered by students like you

Albarellak

Answered question

2021-04-09

Find both first partial derivatives.

z = e^{x y}

Answer & Explanation

Brighton

Skilled2021-04-11Added 103 answers

Step 1
Given function is $z = e^{x y}$ .
Partial derivative of function means derivative of function with respect to one variable keeping other variable as constant.
Partial derivative of given function with respect to x keeping y as constant.
$\frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (e^{x y})$
$= e^{x y} \frac{\partial}{\partial x} (x y)$
$= e^{x y} (1 \cdot y)$
$= y e^{x y}$
Step 2
Partial derivative of given function with respect to y keeping x as constant.
$\frac{\partial z}{\partial y} = \frac{\partial}{\partial y} (e^{x y})$
$= e^{x y} \frac{\partial}{\partial y} (x y)$
$= e^{x y} (x \cdot 1)$
$= x e^{x y}$
Hence, $\frac{\partial z}{\partial x} = y e^{x y} \frac{\partial z}{\partial y} = x e^{x y}$

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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