Resolved: "Find all second-order partial derivatives for the following...."

Jaden Easton

Answered question

2021-05-25

Find all second-order partial derivatives for the following.

k (x, y) = \frac{- 7 x}{2 x + 3 y}

Demi-Leigh Barrera

Skilled2021-05-26Added 97 answers

Step 1
Find all second-order partial derivatives for the following.

k (x, y) = \frac{- 7 x}{2 x + 3 y}

We first find the derivative with respect to x first,

k_{x} (x, y) = \frac{(2 x + 3 y) (- 7) - (- 7 x) (2)}{{(2 x + 3 y)}^{2}}

k_{x} (x, y) = \frac{- 14 x - 21 y + 14 x}{{(2 x + 3 y)}^{2}}

k_{x} (x, y) = \frac{- 21 y}{{(2 x + 3 y)}^{2}}

k_{\times} (x, y) = \frac{{(2 x + 3 y)}^{2} (0) - (- 21 y) 2 (2 x + 3 y) 2}{{(2 x + 3 y)}^{4}}

k_{\times} (x, y) = \frac{84 y}{{(2 x + 3 y)}^{3}}

Step 2
We find the derivative with respect to y,

k_{y} (x, y) = \frac{(2 x + 3 y) (0) - (- 7 x) (3)}{{(2 x + 3 y)}^{2}}

k_{y} (x, y) = \frac{21 x}{{(2 x + 3 y)}^{2}}

k_{y y} (x, y) = \frac{{(2 x + 3 y)}^{2} (0) - (21 x) 2 (2 x + 3 y) 3}{{(2 x + 3 y)}^{4}}

k_{y y} (x, y) = \frac{- 126 x}{{(2 x + 3 y)}^{3}}

Jeffrey Jordon

Expert2021-12-25Added 2605 answers

Answer is given below (on video)

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