Find both first partial derivatives. z=e^{xy}

Albarellak

Albarellak

Answered question

2021-04-09

Find both first partial derivatives. z=exy

Answer & Explanation

Brighton

Brighton

Skilled2021-04-11Added 103 answers

Step 1
Given function is z=exy.
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.
zx=x(exy)
=exyx(xy)
=exy(1y)
=yexy
Step 2
Partial derivative of given function with respect to y keeping x as constant.
zy=y(exy)
=exyy(xy)
=exy(x1)
=xexy
Hence, zx=yexy zy=xexy

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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