Derivative of cos(x)
The derivative of the cosine function, cos(x), can be calculated using the chain rule
The derivative of the cosine function, cos(x), can be calculated using the chain rule.
The chain rule states that if we have a composition of functions, f(g(x)), then the derivative of this composition is given by the product of the derivative of the outer function, f'(g(x)), and the derivative of the inner function, g'(x).
In the case of cos(x), the outer function is cos(u), where u = x, and the inner function is u = x.
The derivative of the outer function cos(u) with respect to u is equal to -sin(u).
The derivative of the inner function u = x with respect to x is equal to 1.
To find the derivative of cos(x), we apply the chain rule:
d/dx (cos(x)) = d/dx (cos(u)) = -sin(u) * d/du (u) = -sin(x) * 1 = -sin(x).
Therefore, the derivative of cos(x) is -sin(x).
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