Find all the second partial derivatives. f(x,y)=x^{4}y-2x^{5}y^{2} f_{xx}(x,y)= f_{xy}(x,y)= f_{yx}(x,y)= f_{yy}(x,y)=

sodni3 2021-05-09 Answered
Find all the second partial derivatives.
f(x,y)=x4y2x5y2
f×(x,y)=
fxy(x,y)=
fyx(x,y)=
fyy(x,y)=
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Expert Answer

bahaistag
Answered 2021-05-10 Author has 101 answers
Step 1
Given function is f(x,y)=x4y2x5y2
Obtain the first partial derivative with respect to x and y.
fx(x,y)=(x4y2x5y2)
=4x3y10x4y2
fy(x,y)=(x4y2x5y2)
=x44x5y
Step 2
Compute the second derivative.
f×(x,y)=(4x3y10x4y2)
=12x2y40x3y2
fxy(x,y)=(4x3y10x4y2)
=4x320x4y
fyx(x,y)=(x44x5y)
=4x320x4y
fyy=(x44x5y)
=04x5
=4x5
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