How do u differentiate a multivariate chain rule?
Answers:
Example:
If z=f(u,v),
u=g(x,y) and
v=h(x,y), then
(all derivatives are supposed to be partial derivatives)
dz/dx=dz/du*du/dx+dz/dv*dv/dx
dz/dy=dz/du*du/dy+dz/dv*dv/dy
Alternatively, you can set of the matrices
[[dz/du dz/dv]]
and
[[ du/dx du/dy]
[dv/dx dv/dy]]
and get that
[[dz/dx dz/dy]]
is the product of the two matrices.
for example?
if you mean something like e^cos(tanx)
=e^costanx*(-sintanx)(sec^2x)
I think you are refering to
f(x,y) and differentiate with respect to t
df(x,y) = df/dx.dx/dt + df/dy.dy.dt where df/dx is partial derivative and not full derivative
one can use this formula
you use partial differentiation
very easy stuff, differentiate each variable alone and hold the others constant
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