Mastering the Chain Rule | Finding the Derivative of Cos(x) Using the Chain Rule

Derivative of cos(x)

The derivative of the cosine function can be found by using the chain rule of differentiation

The derivative of the cosine function can be found by using the chain rule of differentiation. The chain rule states that if we have a composite function, f(g(x)), then the derivative 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 the case of cos(x), the outer function is cosine and the inner function is x. The derivative of the outer function, cosine, is given by the negative sine function, which can be written as -sin(x). The derivative of the inner function, x, is simply 1.

Applying the chain rule, we can find the derivative of cos(x) as follows:

d/dx [cos(x)] = -sin(x) * 1

Simplifying the expression, we get:

d/dx [cos(x)] = -sin(x)

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

In summary, the derivative of cos(x) is equal to -sin(x).

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