Find the first partial derivatives of the following functions. h(x,y)=x-\sqrt{x^{2}-4y}

Jason Farmer

Jason Farmer

Answered question

2021-05-16

Find the first partial derivatives of the following functions.
h(x,y)=xx24y

Answer & Explanation

Cristiano Sears

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,
hx(x,y)=ddxxddxx24y
=112(x24y)121(2x)
=1xx24y
Step 2: Finding the derivative with respect to y
For the derivative with respect to y, derivative of x is 0
Therefore,
hy(x,y)=ddyxddyx24y
=012(x24y)121(4)
=2x24y
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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