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Jason Farmer

Answered question

2021-05-16

Find the first partial derivatives of the following functions.

h (x, y) = x - \sqrt{x^{2} - 4 y}

Cristiano Sears

Skilled2021-05-18Added 96 answers

Step 1: Finding the derivative with respect to x
For the derivative with respect to x, derivative of y is 0.
Therefore,

h_{x} (x, y) = \frac{d}{d x} x - \frac{d}{d x} \sqrt{x^{2} - 4 y}

= 1 - \frac{1}{2} {(x^{2} - 4 y)}^{\frac{1}{2} - 1} (2 x)

= 1 - \frac{x}{\sqrt{x^{2} - 4 y}}

Step 2: Finding the derivative with respect to y
For the derivative with respect to y, derivative of x is 0
Therefore,

h_{y} (x, y) = \frac{d}{d y} x - \frac{d}{d y} \sqrt{x^{2} - 4 y}

= 0 - \frac{1}{2} {(x^{2} - 4 y)}^{\frac{1}{2} - 1} (- 4)

= \frac{2}{\sqrt{x^{2} - 4 y}}

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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