Exploring the Chain Rule: The Derivative of cos(x) and its Application

d/dx(cosx)

To find the derivative of cos(x) with respect to x (d/dx(cosx)), you can use the basic rules of differentiation

To find the derivative of cos(x) with respect to x (d/dx(cosx)), you can use the basic rules of differentiation.

The derivative of cos(x) can be found using the chain rule of differentiation:

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

The chain rule states that if you have a composite function, such as cos(x), you can find its derivative by taking the derivative of the outer function (cos) and multiplying it by the derivative of the inner function (x).

The derivative of the outer function cos(x) is -sin(x). This means that for each value of x, the rate of change of cos(x) is equivalent to -sin(x).

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

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