The following questions are about the function f(x,y)=x^{2}e^{2xy}.

Jaden Easton

Jaden Easton

Answered question

2021-10-08

The following questions are about the function f(x,y)=x2e2xy.
Calculate fx(2,0), and fy(2,0).

Answer & Explanation

casincal

casincal

Skilled2021-10-09Added 82 answers

Step 1
If f(x,y) is a function of two variables x and y, then
fx(x,y)=fx
fy(x,y)=fy
The equation of the tangent plane of function f at the point (x0,y0) is
z=f(x0,y0)+fx(x0,y0)(xx0)+fy(x0,y0)(yy0)
Step 2
We need to find the value of fx(2,0) and fy(2,0).
fx(2,0)=2(2)e2(2)(0)((2)(0)+1)
=4e0(0+1)
=4(1)(1)
=4
And,
fy(2,0)=2(2)3e2(2)(0)
=2(8)e0
=16(1)
=16
Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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