d/dx(cosx)
To find the derivative of cos(x) with respect to x, we can use the differentiation rules
To find the derivative of cos(x) with respect to x, we can use the differentiation rules.
The derivative of cos(x) can be found using the chain rule, which states that if we have a function of the form f(g(x)), the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).
In this case, f(u) = cos(u) and g(x) = x, so we can write the derivative as follows:
d/dx(cos(x)) = d/dx(cos(g(x))) = -sin(g(x)) * g'(x)
Now, g(x) = x, and its derivative g'(x) is simply 1. Therefore, we have:
d/dx(cos(x)) = -sin(x) * 1 = -sin(x)
So, the derivative of cos(x) with respect to x is -sin(x).
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