Mathematics
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OpenStudy (anonymous):
How do you find the second partial derivative of f(x,y)=cos^2^xsin^2^y?
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OpenStudy (anonymous):
its impossible because the formula is wrong
OpenStudy (anonymous):
his yes it is
OpenStudy (anonymous):
were do you get asomthing like that lol
OpenStudy (anonymous):
it's f(x,y)=cos(squared)xsin(squared)y
OpenStudy (anonymous):
answer is 6
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OpenStudy (anonymous):
How did you get that??
OpenStudy (anonymous):
easy you do not know
OpenStudy (anonymous):
no that's why i'm asking... lol
OpenStudy (anonymous):
i can not tell you cuz ther is diff way to do it
OpenStudy (anonymous):
and i do not know how he did it
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OpenStudy (anonymous):
okay thanks
OpenStudy (anonymous):
whats the question
OpenStudy (anonymous):
How do you find the second partial derivative of f(x,y)=cos(squared)xsin(squared)y?
OpenStudy (anonymous):
with respect to what?
OpenStudy (anonymous):
we start with fx, and fy, then we get fxx, fxy, fyx and fyy,
notice that fxy = fyx
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OpenStudy (anonymous):
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OpenStudy (anonymous):
thanks lol
OpenStudy (anonymous):
ok with respect to what
so you want all the partial derivatives?
ok one sec
OpenStudy (anonymous):
with respect to all of them lol
OpenStudy (anonymous):
i will do this on paper
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OpenStudy (anonymous):
thanks a lot
OpenStudy (anonymous):
didnt post?
OpenStudy (anonymous):
how do do a partial derivative in respect to everything?
OpenStudy (anonymous):
nope...
OpenStudy (anonymous):
fx = sin^2 y * 2 cos x (-sin x), treat y as a constant
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OpenStudy (anonymous):
then it is in respect to x
OpenStudy (anonymous):
yes
OpenStudy (anonymous):
thats first partial wrt to x , wrt means with respect to
OpenStudy (anonymous):
fy = cos^2 x * 2 sin y cos y (treat x as a constant)
OpenStudy (anonymous):
oh. ok
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OpenStudy (anonymous):
so what is so difficult about this?
OpenStudy (anonymous):
I didn't know how to do it obviously...
OpenStudy (anonymous):
benito, not nice
OpenStudy (anonymous):
Thanks cantorset!!!
OpenStudy (anonymous):
now we find fxx, fxy, fyx, and fyy
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OpenStudy (anonymous):
whats cool, it turns out fxy = fyx always
OpenStudy (anonymous):
i see
OpenStudy (anonymous):
first fundamental theorem of partial derivatives