Find the four second partial derivatives of f(x, y) = x^2y^3.

Reggie 2021-03-07 Answered
Find the four second partial derivatives of f(x,y)=x2y3.
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Expert Answer

Clelioo
Answered 2021-03-08 Author has 88 answers

Step 1
Given function:
f(x,y)=x2y3
The four-second partial derivatives of f(x,y):fxx,fyy,fxy,fyx
Step 2
Now,
Apply the Power Rule: ddx(xa)=axa1 to find the partial derivatives:
fxx=x(fx)
=x(x2y3x)
=(2xy3x=2y3
fyy=y(fy)
=y(x2y3y))
=(3x2y2y)
=3x2×2y
=6x2y
fxy=y(fx)
=yx2y3x)
=(2xy3y)
=6x2
fyx=x(fy)
=x(x2y3y)
=(3x2y2x)
=6xy2

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