Find the derivative of the function using the derivative rule y = cos3x * ln (2x-3).

| July 19, 2021 | education

Using basic differentiation formulas and differentiation rules:

(x ^ n) ‘= n * x ^ (n-1).

(sin (x)) ‘= cos (x).

(cos (x) ‘= -sin (x).

(c * u) ’= c * u’, where c is const.

(u ± v) ‘= u’ ± v ‘.

(u / v) ’= (u’v – uv’) / v ^ 2

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) ‘= (cos (x) / (3x ^ 2 + 4))’ = ((cos (x)) ‘* (3x ^ 2 + 4) – (cos (x) * (3x ^ 2 + 4) ‘) / (3x ^ 2 + 4) ^ 2 = ((cos (x))’ * (3x ^ 2 + 4) – (cos (x) * ((3x ^ 2) ‘+ (4)’ )) / (3x ^ 2 + 4) ^ 2 = (-sin (x) * (3x ^ 2 + 4) – (cos (x) * (6x + 0)) / (3x ^ 2 + 4) ^ 2 = (-sin (x) * (3x ^ 2 + 4) – 6x * (cos (x)) / (3x ^ 2 + 4) ^ 2.

Answer: The derivative of our given function will be equal to f (x) ‘= (-sin (x) * (3x ^ 2 + 4) – 6x * (cos (x)) / (3x ^ 2 + 4) ^ 2.



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