Calculate the second-order partial derivatives off (x,y)=x^{3}+y^{2}e^{x}

Shelia Lawrence

Shelia Lawrence

Answered question

2021-12-10

Calculate the second-order partial derivatives off (x,y)=x3+y2ex

Answer & Explanation

temnimam2

temnimam2

Beginner2021-12-11Added 36 answers

Step 1
To calculate the second order partial derivatives of the function f(x,y)=x3+y2ex
Step 2
Let us calculate the first order partial derivatives.
fx(x,y)=3x2+y2ex
fy(x,y)=0+ex(2y)=2exy
Step 3
Now we calculate the second order partial derivatives.
fxx(x,y)=3(2x)+y2ex=6x+y2ex
fxy(x,y)=(fy(x,y))x=2exy
fyx(x,y)=(fx(x,y))y=0+(2y)ex=2exy
fyy(x,y)=(fy(x,y))y=2ex

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