Best solutions to - "The following questions are about the function f(x,y)=x2e2xy...."

Jaden Easton

Answered question

2021-10-08

The following questions are about the function

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

.
Calculate

f_{x} (2, 0), and f_{y} (2, 0)

casincal

Skilled2021-10-09Added 82 answers

Step 1
If f(x,y) is a function of two variables x and y, then

f_{x} (x, y) = \frac{\partial f}{\partial x}

f_{y} (x, y) = \frac{\partial f}{\partial y}

The equation of the tangent plane of function f at the point

(x_{0}, y_{0})

z = f (x_{0}, y_{0}) + f_{x} (x_{0}, y_{0}) (x - x_{0}) + f_{y} (x_{0}, y_{0}) (y - y_{0})

Step 2
We need to find the value of

f_{x} (2, 0) and f_{y} (2, 0)

f_{x} (2, 0) = 2 (2) e^{2 (2) (0)} ((2) (0) + 1)

= 4 e^{0} (0 + 1)

=4(1)(1)
=4
And,

f_{y} (2, 0) = 2 {(2)}^{3} e^{2 (2) (0)}

= 2 (8) e^{0}

=16(1)
=16

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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