derivative of cosx
The derivative of the cosine function, denoted as cos(x), can be found by applying the chain rule
The derivative of the cosine function, denoted as cos(x), can be found by applying the chain rule. The chain rule states that if we have a composite function f(g(x)), then its derivative is given by f'(g(x)) * g'(x).
In the case of cos(x), we can consider it as a composite function where the inner function is x and the outer function is cos. Therefore, we need to find the derivative of the outer function and multiply it by the derivative of the inner function.
The derivative of the outer function cos(x) is -sin(x). This derivative can be obtained by recalling the standard derivative results for trigonometric functions.
Now, we need to multiply the derivative of the outer function by the derivative of the inner function, which is 1, since the derivative of x is 1.
Putting it all together, we have:
Derivative of cos(x) = -sin(x) * 1 = -sin(x)
So, the derivative of cos(x) is equal to -sin(x).
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