Check the solution to "Let z=4x2−8×y4+7y5−3. Find all the first and second..." - Plainmath

mattgondek4

Answered question

2021-09-27

Let

z = 4 x^{2} - 8 \times y^{4} + 7 y^{5} - 3

. Find all the first and second order partial derivatives of z.

Answer & Explanation

likvau

Skilled2021-09-28Added 75 answers

Step 1
Given that

z = 4 x^{2} - 8 y^{4} + 7 y^{5} - 3

Then first-order partial derivatives are,

\frac{\partial z}{\partial x} = 8 x

\frac{\partial z}{\partial y} = - 32 y^{3} + 35 y^{4}

Step 2
Second-order partial derivates are,

\frac{\partial^{2} z}{\partial x^{2}} = 8

\frac{\partial^{2} z}{\partial y^{2}} = - 96 y^{2} + 140 y^{3}

\frac{\partial^{2} z}{\partial x \partial y} = 0

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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