Understanding the Chain Rule | Finding the Derivative of Cos(x) with Respect to x

d/dx(cos(x))

To find the derivative of the function cos(x) with respect to x (denoted as d/dx(cos(x))), we can use the rules of differentiation

To find the derivative of the function cos(x) with respect to x (denoted as d/dx(cos(x))), we can use the rules of differentiation.

The derivative of cos(x) can be found using the chain rule. The chain rule states that if we have a composition of functions, then the derivative is given by the derivative of the outer function multiplied by the derivative of the inner function.

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 1.

Therefore, applying the chain rule, the derivative of cos(x) with respect to x is:
d/dx(cos(x)) = -sin(x) * 1 = -sin(x).

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

In summary:
d/dx(cos(x)) = -sin(x).

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