How to Find the Derivative of cos(x) Using the Chain Rule

d/dx(cosx)

sinx

To find the derivative of the function f(x) = cos(x) with respect to x (denoted as d/dx(cosx)), we can apply the chain rule of differentiation.

The chain rule states that if we have a composition of functions, such as f(g(x)), then the derivative of this composition is given by the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

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

d/dx(cosx) = -sin(x) * d/dx(x)

The derivative of x with respect to x is simply 1. Therefore, we can simplify the expression as:

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

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

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