d/dx [ cos(f(x)) ]
-sin(f(x))*f'(x)
To find the derivative of cos(f(x)), we can use the chain rule.
Recall that the chain rule states that if y = f(g(x)), then
(dy/dx) = (dy/du) * (du/dx)
where u = g(x).
In this case, let u = f(x). Therefore,
(cos(f(x)))’ = (cos(u))’ * (du/dx)
Now, we just need to find each part of this equation.
(cos(u))’ = -sin(u)
And,
(du/dx) = f'(x)
Therefore,
(cos(f(x)))’ = -sin(f(x)) * f'(x)
So the final answer is:
d/dx [ cos(f(x)) ] = -sin(f(x)) * f'(x)
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