## Derivative of cos x

### The derivative of the function cosine of x, denoted as cos(x), can be found using the chain rule of differentiation

The derivative of the function cosine of x, denoted as cos(x), can be found using the chain rule of differentiation.

The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x can be found by multiplying the derivative of f with respect to u and the derivative of g with respect to x.

In the case of cos(x), we can identify f(u) as cos(u) and u as x. So, applying the chain rule, we have:

dy/dx = d/dx [cos(u)] * d/dx [x]

To find the derivative of cos(u), which is the derivative of cos(x), we use the trigonometric identity: d/dx [cos(x)] = -sin(x).

Therefore, dy/dx = -sin(u) * 1 = -sin(x).

Hence, the derivative of the cosine function is -sin x.

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