Question: "Find all of the first order partial derivatives..."

Cabiolab

Answered question

2021-10-15

Find all of the first order partial derivatives

f (x, y) = x^{4} + 6 \sqrt{y} - 10

rogreenhoxa8

Skilled2021-10-16Added 109 answers

Step 1: Consider the provided function,

f (x, y) = x^{4} + 6 \sqrt{y} - 10

Partially differentiate the function with respect to x.

f_{x} = \frac{\partial}{\partial x} (x^{4} + 6 \sqrt{y} - 10)

= 4 x^{4 - 1}

= 4 x^{3}

Step 2: Again, Partially differentiate the function with respect to y.

f_{y} = \frac{\partial}{\partial y} (x^{4} + 6 \sqrt{y} - 10)

= 6 \frac{\partial}{\partial y} {(y)}^{\frac{1}{2}}

= 6 \cdot \frac{1}{2} {(y)}^{1 - \frac{1}{2}}

= \frac{3}{\sqrt{y}}

Therefore, the all partial derivative of first order is

4 x^{3} and \frac{3}{\sqrt{y}}

respectively.

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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