Solved: "Find the four second-order partial derivatives. f(x,y)=3x7y−4xy+8y f×(x,y)="

Bergen

Answered question

2021-05-07

Find the four second-order partial derivatives.

f (x, y) = 3 x^{7} y - 4 x y + 8 y

f_{\times} (x, y) =

Gennenzip

Skilled2021-05-08Added 96 answers

Step 1
Given

f (x, y) = 3 x^{7} y - 4 x y + 8 y

Step 2

f_{x} = \frac{\partial}{\partial x} (3 x^{7} y - 4 x y + 8 y)

= 21 x^{6} y - 4 y

f_{\times} = \frac{\partial}{\partial x} (21 x^{6} y - 4 y)

f_{\times} = 126 x^{5} y

Step 3

f_{y} = \frac{\partial}{\partial y} (3 x^{7} y - 4 x y + 8 y)

f_{y} = 3 x^{7} - 4 x + 8

f_{y y} = \frac{\partial}{\partial y} (3 x^{7} - 4 x + 8)

f_{y y} = 0

f_{x y} = \frac{\partial}{\partial x} (3 x^{7} - 4 x + 8)

f_{x y} = 21 x^{6} - 4

f_{y x} = \frac{\partial}{\partial y} (21 x^{6} y - 4 y)

f_{y x} = 21 x^{6} - 4

Step 4

\Rightarrow f_{\times} = 126 x^{5} y, f_{y y} = 0

f_{x y} = 21 x^{6} - 4, f_{y x} = 21 x^{6} - 4

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?