Derivative of cos(x) with respect to x | Calculating the Change in Trigonometric Function

d/dx cos(x)

The expression “d/dx” represents the derivative operator, which is used to find the derivative of a function with respect to the variable x

The expression “d/dx” represents the derivative operator, which is used to find the derivative of a function with respect to the variable x. In this case, we are asked to find the derivative of the function cos(x).

To find the derivative of cos(x), we can use the derivative rules. The derivative of cos(x) can be found by applying the chain rule. The chain rule states that if we have a composition of functions, such as cos(u), then the derivative is given by the derivative of the outer function times the derivative of the inner function.

In this case, the outer function is cos(u), where u = x, and the inner function is u = x. The derivative of the outer function is given by -sin(u), and the derivative of the inner function is 1. Therefore, by applying the chain rule, we find:

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

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

Note: The derivative of cos(x) is derived using the fundamental trigonometric identities and the definition of the derivative. Alternatively, one can also use the power series expansion of cos(x) to find its derivative.

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