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Answered question

2021-04-14

Find the four second partial derivatives of the following function.
$z = 3 y e^{7 x}$
$z_{x x} =$ ?

Answer & Explanation

estenutC

Skilled2021-04-16Added 81 answers

Step 1
The four-second partial derivatives of function z=f(x,y),
$z_{x x}, z_{y y}, z_{x y}, z_{y x}$
Step 2
Given: $z = 3 y e^{7 x}$ (i)
Differentiate both sides with respect to x, we get
$z_{x} = 3 y (7) e^{7 x} = 21 y e^{7 x}$ (ii)
$z_{x x} = 21 y (7) e^{7 x}$
i.e. $z_{x x} = 147 y e^{7 x}$
Differentiate (ii) with respect to y, we get
$z_{y} = 3 e^{7 x}$ (iii)
$\Rightarrow z_{y y} = 0$
Differentiate (iii) with respect to x , we get
$z_{y x} = 3 (7) e^{7 x} = 21 e^{7 x}$
i.e. $z_{y x} = 21 e^{7 x}$
Step 3
The four-second partial derivatives:
$z_{x x} = 147 y e^{7 x}$
$z_{x y} = 21 e^{7 x}$
$z_{y y} = 0$
$z_{y x} = 21 e^{7 x}$

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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