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Please tell me where this reasoning is wrong, because I know it is but I can't see how.

f(x) = sinx

f ' (x) = cosx

f(60) = sin 60

f ' (60) = cos 60

but

g(x) = sin 2x

g'(x) = 2 cos 2x

set x = 30

then: g(30) = sin 60

g'(x) = 2 cos 60

but

f(60) = g(30)

so f ' (60) = g'(30)

i.e cos 60 = 2 cos 60

thus: 1 = 2

WHY!!!!! HOW!!!!!

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# Derivative of sin^2x

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