Find the four second partial derivatives of the following function.z=3ye^{7x}z_{xx}=ZKS?

Anonym

Anonym

Answered question

2021-04-14

Find the four second partial derivatives of the following function.
z=3ye7x
zxx=?

Answer & Explanation

estenutC

estenutC

Skilled2021-04-16Added 81 answers

Step 1
The four-second partial derivatives of function z=f(x,y),
zxx,zyy,zxy,zyx
Step 2
Given: z=3ye7x(i)
Differentiate both sides with respect to x, we get
zx=3y(7)e7x=21ye7x(ii)
zxx=21y(7)e7x
i.e. zxx=147ye7x
Differentiate (ii) with respect to y, we get
zy=3e7x(iii)
zyy=0
Differentiate (iii) with respect to x , we get
zyx=3(7)e7x=21e7x
i.e. zyx=21e7x
Step 3
The four-second partial derivatives:
zxx=147ye7x
zxy=21e7x
zyy=0
zyx=21e7x

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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