Using basic differentiation formulas and differentiation rules:
(x ^ n) ‘= n * x ^ (n-1).
(e ^ x) ‘= e ^ x.
(cos (x) ‘= -sin (x).
(c * u) ’= c * u’, where c is const.
(u ± v) ‘= u’ ± v ‘.
(uv) ‘= u’v + uv’.
y = f (g (x)), y ‘= f’u (u) * g’x (x), where u = g (x).
Thus, the derivative of our given function will look like this:
f (x) ‘= (x * cos (x))’ = (x) ‘* cos (x) + x * (cos (x))’ = 1 * cos (x) + x * (-sin (x )) = cos (x) – x * sin (x).
Answer: The derivative of our given function will be equal to f (x) ‘= cos (x) – x * sin (x).
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