(d/dx) cosx =
To find the derivative of cos(x) with respect to x, denoted as (d/dx) cos(x), we can use the chain rule
To find the derivative of cos(x) with respect to x, denoted as (d/dx) cos(x), we can use the chain rule. The chain rule states that if we have a composite function f(g(x)), then the derivative of f(g(x)) with respect to x is given by the product of the derivative of f with respect to g multiplied by the derivative of g with respect to x.
In this case, cos(x) is a composite function where the outer function is cos and the inner function is x. The derivative of cos(x) with respect to x is then given as follows:
(d/dx) cos(x) = (d/dx)(cos(u)) * (d/dx) x = -sin(x) * 1 = -sin(x),
where u = x and we use the fact that the derivative of x with respect to x is 1.
Therefore, the derivative of cos(x) with respect to x is -sin(x).
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