For the following sets of variables, find all the relevant second derivatives. In all cases, first find general expressions for the second derivatives and then substitute variables at the last step. f(x,y)=x^2y-xy^2,where x = st and y = s/t

DofotheroU 2020-11-29 Answered

For the following sets of variables, find all the relevant second derivatives. In all cases, first find general expressions for the second derivatives and then substitute variables at the last step. f(x,y)=x2yxy2,where x=standy=st

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Expert Answer

Asma Vang
Answered 2020-11-30 Author has 93 answers

Step 1
Given function is f(x,y)=x2yxy2 where x=st,y=s.
The all relevant second derivatives are fxx,fyy,fxy,fyx.
Step 2
Find partial derivative with respect to x for the function f(x,y)=x2yxy2.
fx=2xyy2
Find partial derivative with respect to y for the function f(x,y)=x2yxy2.
fy=x22xy
Differentiate function fx=2xyy2 withe respect to x to get f×.
fxx=2y
Substitute y=stfxx=2y.
fxx=2st
Differentiate function fy=x22xy with respect to y to get fyy.
fyy=2x
Substitute x=st in fyy=2x.
fyy=2st
Differentiate function fy=x22xy with respect to x to get fxy.
fxy=2x2y
Substitute x=st,y=sfxy=2x2y.
fxy=2st2st
Differentiate function fx=2xyy2 with respect to y to get fyx.
fyx=2x2y
Substitute x=st,y=sfyx=2x2y
fyx=2st2st.
Step 3
Therefore, all relevant second derivatives of function

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Jeffrey Jordon
Answered 2022-01-30 Author has 2064 answers

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