$\frac{d}{ds}$ f(s)

This function is also said to be the derivative or differentiation with respect to‘s’. In mathematics some of the cases, the differentiation of a function f (s) is said to be differentiation coefficient of f (s).

Let’s talk about the Derivative of Cosine;

Here cosine and cos both the word having same meaning, let see the derivative of cosine.

Cosine (s) = - sine (s);

Now we will see the proof of Derivative of Cosine;

First we write the cosine (s) in the derivative form:

d / dx cosine (s) = - sine (s);

Here we have to apply the Chain Rule for finding the derivative of cosine (s).

In mathematics, Chain rule is used to differentiate compositions of Functions. The chain rule is given by:

D f (g(s)) = f’ (g (s)) g’(s); on applying we can write it as:

→ Cosine (s) = sine (s + π / 2); in the derivative form we can write it as:

→ $\frac{d}{ds}$ cosine (s) = $\frac{d}{ds}$ sine (s + π / 2);

On further solving we get:

→$\frac{d}{ds}$ sine (u) * $\frac{d}{ds}$ ( s + π / 2) (put u = s + π / 2);

We know that differentiation of sine s = cosine s, so put in the above expression.

= cosine (s) * 1 = cosine (s + π / 2);

On further solving we get – sine (s).

This is how to find the Derivative of Cosine.