d/dx [ cos(x) ]
To find the derivative of the function cos(x) with respect to x, we can use the chain rule
To find the derivative of the function cos(x) with respect to x, we can use the chain rule. The chain rule states that if we have a composition of functions, f(g(x)), then the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).
In this case, we have f(x) = cos(x) and g(x) = x.
So, let’s find the derivative using the chain rule:
f'(x) = -sin(x) (The derivative of cos(x) is -sin(x))
g'(x) = 1 (The derivative of x is 1)
Now, applying the chain rule, we have:
d/dx [cos(x)] = f'(g(x)) * g'(x)
= (-sin(x)) * (1)
= -sin(x)
Therefore, the derivative of cos(x) with respect to x is -sin(x).
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