Derivative of cosx
The derivative of cos(x) can be found using the chain rule
The derivative of cos(x) can be found using the chain rule. The chain rule states that if we have a composite function, such as f(g(x)), then the derivative of this function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.
In this case, we have f(x) = cos(x), which is the outer function, and g(x) = x, which is the inner function. So, we can use the chain rule to find the derivative of f(g(x)) = cos(x).
The derivative of f(g(x)) with respect to x is given by:
(d/dx) [cos(g(x))] = -sin(g(x)) * g'(x)
Here, g'(x) represents the derivative of g(x), which is equal to 1.
So, substituting g(x) = x and g'(x) = 1 into the formula, we get:
(d/dx) [cos(x)] = -sin(x) * 1
Thus, the derivative of cos(x) is equal to -sin(x).
Therefore, d/dx[cos(x)] = -sin(x).
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