## derv sin(x)

### To find the derivative of sin(x), we will use the chain rule

To find the derivative of sin(x), we will use the chain rule.

The chain rule states that if we have a function g(u) and another function f(x), the derivative of the composition of f(g(x)) is given by f'(g(x)) times g'(x).

In this case, g(x) = sin(x) and f(x) = x. So, we can rewrite sin(x) as g(u) and x as f(u).

Now, let’s find the derivative of g(u), which is g'(u). Since g(u) = sin(u), the derivative of g(u) (or g'(u)) is given by cos(u).

Next, let’s find the derivative of f(x), which is f'(x). Since f(x) = x, the derivative of f(x) (or f'(x)) is simply 1.

Now, applying the chain rule, we can find the derivative of sin(x):

derv(sin(x)) = f'(g(x)) * g'(x)

= 1 * cos(x)

= cos(x).

Therefore, the derivative of sin(x) is cos(x).

In summary:

derv(sin(x)) = cos(x)

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