d/dx(cosx)
To find the derivative of the function f(x) = cos(x) with respect to x, we can use the derivative rules
To find the derivative of the function f(x) = cos(x) with respect to x, we can use the derivative rules.
The derivative, denoted as d/dx or f'(x), represents the rate of change of a function with respect to its independent variable, x. In this case, we want to find the derivative of the cosine function.
The derivative of cos(x) can be found using the chain rule, which states that for a composition of functions, the derivative is the product of the derivative of the outer function with the derivative of the inner function.
The outer function here is cos(x), and the inner function is x. The derivative of the outer function with respect to its variable is -sin(x), while the derivative of the inner function with respect to its variable is 1.
Therefore, by applying the chain rule, we can find the derivative of cos(x) as follows:
d/dx(cosx) = -sin(x) * 1
Simplifying the equation, we get:
d/dx(cosx) = -sin(x)
So, the derivative of cos(x) with respect to x is -sin(x).
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