# Simple question about differentiation of trigonometric function

• B
lioric

Explain to me:

Why the 2πf came in front?

I lost touch and sort of forgot.

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## Answers and Replies

soarce
This is the derivation differentiation chain rule: $$\frac{df(g(x))}{dx}=\frac{df}{dg}\cdot\frac{dg}{dx}$$
Edited by mentor...

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lioric
could you please show me how this works with my example

soarce
In your case ##x=t##, ##f(x)=cos(x)##, ##g(x)=2\pi f x## and ##f(g(x))=(f\circ g)(x)=cos(2\pi f x)##.

Mentor
Another way to demonstrate it is:

##d/dt ( cos (2 * \pi * f * t) ) = ##

## = - sin ( 2 * \pi * f * t ) * d/dt ( 2 * \pi * f * t ) ##

## = - sin ( 2 * \pi * f * t ) * ( 2 * \pi * f ) ##

## = - ( 2 * \pi * f * t ) * sin ( 2 * \pi * f * t ) ##

Science Advisor
General formula. Let f'(x)=g(x), then f'(ax)=ag(ax).