Write first and second partial derivativesf(x,y)=2xy+9x^2y^3+7e^(2y)+16a)f_xb)f_(xx)c)f_(xy)d)f_ye)f_(yy)

Joni Kenny 2021-02-02 Answered

Write first and second partial derivatives
f(x,y)=2xy+9x2y3+7e2y+16
a)fx
b)fxx
c)fxy
d)fy
e)fyy
f)fyx

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Expert Answer

unett
Answered 2021-02-03 Author has 119 answers

a) fx=x[2xy+9x2y3+7e2y+16]
fx=2y+18xy3+0+0=2y+18xy3
fx=2y+18xy3
b) fxx=fxx=x[9y+18xy3]
=0+18y3=18y3
fxx=18y3
с) fxy=fxy=y[2y+18xy3]
fxy=2+18x3y2
fxy=2+54x62
d) fy=fy=y[2xy+9x2y3+4e2y+16]
fy=2x+9x23y2+72e2y+0
fy=9x+27x2y+14e2y
e) fyy=y[2x+27x2y2+14e2y
=0+27x2xy2+142e2y
fyy=54x22y+28e2y
f) fyx=fyx=x[2x+27xy2+14e2y]
fyy=2=54xy2

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