Mastering the Chain Rule: Simplifying the Derivative of cos(x)

d/dx cos(x)

To find the derivative of cos(x), we can use the chain rule

To find the derivative of cos(x), we can use the chain rule. The chain rule states that if we have a composition of functions, such as f(g(x)), then the derivative is given by the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

In this case, our outer function is cos(x), and our inner function is x (since x is the argument of the cosine function).

The derivative of the outer function cos(x) is given by -sin(x). This means that when we take the derivative of cos(x), we just need to multiply it by -sin(x).

Therefore, the derivative of cos(x) is -sin(x). So, d/dx cos(x) = -sin(x).

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