Expert answers to "Find all first partial derivatives, and evaluate each..." - Plainmath

ediculeN

Answered question

2021-01-30

Find all first partial derivatives, and evaluate each at the given point.

f (x, y) = x^{2} - y, (0, 2)

Answer & Explanation

Theodore Schwartz

Skilled2021-01-31Added 99 answers

Step 1
The given function is

f (x, y) = x^{2} - y

and a point is (0, 2).
Compute the partial derivatives as follows.

f_{x} (x, y) = \frac{\partial}{\partial x} (x^{2} - y)

= 2 x - 0

= 2 x

f_{y} (x, y) = \frac{\partial}{\partial y} (x^{2} - y)

= 0 - 1 = - 1

Thus, the first partial derivatives are

f_{x} = 2 x and f_{y} = - 1

.
Step 2
Substitute

(x, y) = (0, 2) \in f_{x} = 2 x and f_{y} = - 1

and obtain that,

f_{x} (0, 2) = 0 and f_{y} (0, 2) = - 1

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