How to Find the Derivative of cos(x) Using the Chain Rule – Step by Step Guide

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 the composition of two functions f(g(x)), then the derivative is given by f'(g(x)) * g'(x).

In this case, we have the function f(x) = cos(x), and g(x) = x. So, applying the chain rule, we have:

𝑑/𝑑𝑥[cos 𝑥] = f'(g(x)) * g'(x).

The derivative of f(x) = cos(x) is simply the negative sine function, so f'(x) = -sin(x).

The derivative of g(x) = x is 1 since the derivative of x with respect to x is always 1.

Now, substituting these values into the chain rule formula, we get:

𝑑/𝑑𝑥[cos 𝑥] = -sin(x) * 1 = -sin(x).

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

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