SECTION 3.5: Derivatives of Periodic Functions

It is important to note that since sine and cosine functions are periodic, there derivatives must also be periodic. 

Graphically, it has been proven that if x is the radius,

d/dx(sin x) = cos x  and d/dx (cos x) = -sin x

If differentiating a function within a function, assuming the inside function is z and the outside function is sin or cos,

the d/dx (sin z) = cos z * (dz/dx)  and  d/dx (cos z) = - sin z * (dz/dx)

If k is a constant then,

d/dx (sin kx) = k *cos (kx)  and  d/dx (cos kx) = - k*sin (kt)

Again it is difficult to understand exactly why the following functions are applicable without seeing the theoretical proof for the derivations. But it will definitely be useful to know when working with differentiation of functions.