Find all first partial derivatives, and evaluate each at the given point. f(x,y)=x^2-y,(0,2)

ediculeN 2021-01-30 Answered
Find all first partial derivatives, and evaluate each at the given point. f(x,y)=x2y,(0,2)
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Expert Answer

Theodore Schwartz
Answered 2021-01-31 Author has 99 answers
Step 1
The given function is f(x,y)=x2y and a point is (0, 2).
Compute the partial derivatives as follows.
fx(x,y)=x(x2y)
=2x0
=2x
fy(x,y)=y(x2y)
=01=1
Thus, the first partial derivatives are fx=2xandfy=1.
Step 2
Substitute (x,y)=(0,2)fx=2xandfy=1 and obtain that,
fx(0,2)=0andfy(0,2)=1
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