"Find the first partial derivatives of the given..." was answered by our experts

Cem Hayes

Answered question

2021-02-20

Find the first partial derivatives of the given functions with respect to each independent variable.

f (x, y) = {(2 x - 4)}^{4}

Bentley Leach

Skilled2021-02-22Added 109 answers

Step 1
Given:

f (x, y) = {(2 x - 4)}^{4}

Step 2
The partial derivative of given function f with respect to independent variable x is given below:

f (x, y) = {(2 x - 4)}^{4}

\frac{\partial f}{\partial x} = 4 {(2 x - 4)}^{3} \frac{d}{d x} (2 x - 4)

\frac{\partial f}{\partial x} = 4 {(2 x - 4)}^{3} (2)

\frac{\partial f}{\partial x} = 8 {(2 x - 4)}^{3}

Step 3
The partial derivative of given function f with respect to independent variable y is given below:

f (x, y) = {(2 x - 4)}^{4}

As the given function have only x in the expression. So.

\frac{\partial f}{\partial y} = 0

Step 4
Answer:

\frac{\partial f}{\partial x} = 8 {(2 x - 4)}^{3}

\frac{\partial f}{\partial y} = 0

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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