The Chain Rule | Finding the Derivative of cos(x) with Respect to x

d/dx[cos(x)]

To find the derivative of the function f(x) = cos(x) with respect to x, we use the derivative rules

To find the derivative of the function f(x) = cos(x) with respect to x, we use the derivative rules. In this case, we can apply the chain rule.

The chain rule states that if we have a composite function g(h(x)), then the derivative of g(h(x)) with respect to x is equal to g'(h(x)) * h'(x), where g'(h(x)) represents the derivative of the outer function and h'(x) represents the derivative of the inner function.

In our case, g(x) = cos(x) and h(x) = x. The derivative of the outer function g(x) = cos(x) is -sin(x), and the derivative of the inner function h(x) = x is 1.

Now, we can apply the chain rule:

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

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

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