I'm able to do part A and B, but part C is tripping me up
#Partial Derv, Part C?
surreal spade
you would take the derivative relative to x, and then the derivative relative to y of that:
∂/∂y(∂f/∂x)
and if the function is continuous, as well as the partial derivative relative to x, and the partial derivative relative to y, then that should be the same as ∂/∂x(∂f/∂y)
@lost oyster
surreal spade
the detail I added about continuity links into mean value theorem, when you get to real analysis then you'll learn about how it works and why it's related with calc
lost oyster
ohhh
lost oyster
np
I put it into a calc and it gave me -6x? But when I did it on paper I got 8x^3 -6x
It's the 3rd line
From the top
surreal spade
one sec:
first derivative relative to x:
(-2x)(y-2x²)-(4x)(y-x²)
derivative relative to y:
-2x-4x
I used product rule first
lost oyster
one sec:
first derivative relative to x:
(-2x)(y-2x²)-(4x)(y-x²)
derivative rela...
I go that for the first derv, then simplified down to 8x^3-6xy
surreal spade
-2xy+4x³-4xy+4x²
8x³-6xy
and then relative to y
8x³ is constant, so is 0
-6xy→-6x
lost oyster
wait
surreal spade
what
surreal spade
now you have ∂³f/∂x∂y²
lost oyster
OHHH
surreal spade
yes lmao
lost oyster
I wasn't using the given f(x,y) lmao