Mathematics 76 Online
OpenStudy (anonymous):

How do you find the second partial derivative of f(x,y)=cos^2^xsin^2^y?

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):

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

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

OpenStudy (anonymous):

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

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

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

whats cool, it turns out fxy = fyx always

OpenStudy (anonymous):

i see

OpenStudy (anonymous):

first fundamental theorem of partial derivatives

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