Find the four second partial derivatives. Observe that the second mixed partials are equal. z=e^{x}\tan y

Kyran Hudson

Kyran Hudson

Answered question

2021-02-27

Find the four second partial derivatives. Observe that the second mixed partials are equal.
z=extany

Answer & Explanation

Latisha Oneil

Latisha Oneil

Skilled2021-03-01Added 100 answers

Step 1
To find second partial derivatives of z=extan(y)
Step 2
Differentiate z with respect to x
zx=extan(y)
Differentiate z with respect to y
zy=exsec2(y)
Step 3
Differentiate zx with respect to x
zxx=extan(y)
Differentiate zy with respect to x
zyx=exsec2(y)...(1)
Step 4
Differentiate zx with respect to y
zxy=exsec2(y)...(2)
Differentiate z with respect to y
zyy=ex[2sec(y)][sec(y)tan(y)]
zyy=2exsec2(y)tan(y)
From(1) and (2)
zxy=zyx

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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