Proving the derivative of sin(x)

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This file shows a classic proof that d/dx sin x = cos x
From this you can then also derive quickly the derivatives of the other trigonometric functions.
d/dx cos x = -sin x
d/dx tan x = sec2 x
d/dx cot x = -csc2 x
d/dx sec x = sec x tan x
d/dx csc x = -csc x cot x


f'(x) = Lim dx --> 0 of [f(x+dx)-f(x)]/dx
Sin(x+dx) = Sin(x)*Cos(dx)+Sin(dx)*Cos(x)
Lim dx --> 0 of [Sin(x+dx)-Sin(x)]/dx = Lim dx --> 0 of [Sin(x)*Cos(dx)+Sin(dx)Cos(x)-Sin(x)]/dx
Lim dx --> 0 of [Sin(x)*{Cos(dx)-1}+Sin(dx)Cos(x)]/dx = Lim dx --> 0 of Sin(x)*{Cos(dx)-1}/dx + Sin(dx)*Cos(x)/dx
Lim dx --> 0 of Sin(x){Cos(dx)-1}/dx = 0 and Lim dx --> 0 of Cos(x)*Sin(dx)/dx = 1*Cos(x) or just Cos(x)
So the derivative of Sin(x) is Cos(x)dx