cos(x)’ =
To find the derivative of cos(x), we can make use of the chain rule
To find the derivative of cos(x), we can make use of the chain rule. The chain rule states that if we have a composition of functions, such as f(g(x)), then the derivative of the composition can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.
In this case, we have f(x) = cos(x), where the outer function is f(x) = cos(x) and the inner function is g(x) = x.
The derivative of the outer function cos(x) is found by differentiating the cosine function, which is -sin(x).
The derivative of the inner function g(x) = x is simply 1.
Applying the chain rule, we have:
(cos(x))’ = (-sin(x))(1)
Simplifying this expression gives:
(cos(x))’ = -sin(x)
Therefore, the derivative of cos(x) is -sin(x).
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