Understanding the Chain Rule | Derivative of cos(x) using Differentiation Techniques

cos(x) derivative

To find the derivative of cos(x), we can use the differentiation rules

To find the derivative of cos(x), we can use the differentiation rules. The derivative measures the rate of change of a function with respect to its variable, in this case, x.

The derivative of cos(x) can be determined using the chain rule, which states that the derivative of a composite function f(g(x)) is given by the product of the derivative of the outer function f'(g(x)) and the derivative of the inner function g'(x).

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

The derivative of the outer function cos(x) is -sin(x) and the derivative of the inner function x is simply 1.

Using the chain rule formula, we can find the derivative of cos(x):
(cos(x))’ = -sin(x) * 1 = -sin(x)

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

This means that the rate of change of the cosine function with respect to x at any given point x is given by the negative sine function evaluated at that point x.

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