Math2.org Math Tables: Chain Rule |
(Math) |
f(g(x)) = f(g) * g(x) |
We can use the definition of the derivative:
Therefore, f(g(x)) can be written as such:
f(x) = lim
^{d-->0}f(x+d)-f(x)
d
f(g(x)) = df/dx = (f(g(x+d) - f(g(x))/d
df/dx * 1/(dg/dx) = [ (f(g(x+d) - f(g(x))/d ] * [ d/(g(x+d) - g(x)) ]
= ( f(g(x+d))-f(g(x)) )/(g(x+d)-g(x)) = df/dg
df/dx = df/dg * dg/dx