# Find the derivative of the function y = sin ^ 2 x.

July 22, 2021 | education

| Let’s find the derivative of our given function: f (x) = sin ^ 2 (x).

Using the basic formulas and rules of differentiation:

(x ^ n) ‘= n * x ^ (n-1).

(sin x) ‘= cos x.

(c * u) ’= c * u’, where c is const.

(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 be as follows:

f (x) ‘= (sin ^ 2 (x))’ = (sin (x)) ‘* (sin ^ 2 (x))’ = cos (x) * 2 * sin ^ (2 – 1) (x ) = cos (x) * 2 * sin ^ (1) (x) = cos (x) * 2 * sin (x) = 2cos (x) sin (x).

Using the double angle formula (sin (2x) = 2cos (x) sin (x)), we get:

f (x) ‘= 2cos (x) sin (x) = sin (2x).

Answer: The derivative of our given function will be equal to f (x) ‘= 2cos (x) sin (x) = sin (2x).

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