Understanding the Derivative of cos(x) and its Calculation Method through the Chain Rule.

(d/dx) cos(x)

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

To find the derivative of cos(x) with respect to x, we can use the chain rule. The derivative of cos(x) is obtained by multiplying the derivative of the inside function (x) with the derivative of the outside function (cos(x)).

The derivative of cos(x) with respect to x, denoted as (d/dx) cos(x), can be found as follows:

Using the chain rule, we differentiate the outside function cos(x) and multiply it with the derivative of the inside function x (which is 1):

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

Hence, the derivative of cos(x) with respect to x is:

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

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

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