The Derivative of the Cosine Function | How to Find and Simplify cos'(x)

derivative of cos(x)

The derivative of the cosine function, cos(x), can be found using the basic trigonometric identities and rules of differentiation

The derivative of the cosine function, cos(x), can be found using the basic trigonometric identities and rules of differentiation.

The derivative of a function represents the rate at which the function is changing at a particular point. For the cosine function, let’s denote the derivative of cos(x) as d(cos(x))/dx or simply cos'(x).

To find cos'(x), we can use the chain rule of differentiation. The chain rule states that if we have a composite function, such as f(g(x)), the derivative can be found by taking the derivative of the outer function and then multiplying it by the derivative of the inner function.

In this case, the composite function is cos(x). The outer function is cosine and the inner function is x.

The derivative of the outer function, cosine, is negative sine, represented as -sin(x).

The derivative of the inner function, x, with respect to x is simply 1.

Applying the chain rule, we get:

cos'(x) = -sin(x) * 1

Simplifying, we have:

cos'(x) = -sin(x)

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

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