Find the derivative of the function f (x) = 2sin (2,5x-2)

Let’s find the derivative of our given function: f (x) = sin (6x ^ 4 – 2x ^ 2 + 3).

Using the basic formulas and rules of differentiation:

(x ^ n) ‘= n * x ^ (n-1).

(sin (x)) ’= cos (x).

(c) ‘= 0, where c is const.

(c * u) ’= c * u’, where c is const.

(u ± v) ‘= u’ ± v ‘.

y = f (g (x)), y ’= f’u (u) * g’x (x), where u = g (x).

Thus, the derivative of our given function will be as follows:

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

Answer: The derivative of our given function will be equal to f (x) ‘= (6 * 4 * x ^ 3 – 2 * 2 * x + 0) * cos (6x ^ 4 – 2x ^ 2 + 3).