I need help with differentiation.
I don't quite understand what is derivative of y with respect to some function. Yes x is also a function but let me show the example.
if y = x^2 + 2, what is derivative of y with respect to (1-x) ?
I need help with differentiation.
I don't quite understand what is derivative of y with respect to some function. Yes x is also a function but let me show the example.
if y = x^2 + 2, what is derivative of y with respect to (1-x) ?
I've never heard of such a thing. Are you perhaps supposed to do some sort of substitution, like "u = 1 - x"? So then x = 1 - u, and x^2 + 2 = u^2 - 2u + 3? And then you differentiate with respect to u, and then maybe back-substitute?
I'm just guessing....
You can differentiate any (differentiable) function with respect to any other (differentiable) function. Let f(x) and g(x) be differentiable functions of x. By the chain rule, .
Here and . and so .
The derivative of f with respect to g essentially tells how fast f is increasing or decreasing compared to how fast g is.