Calculate Derivatives of a Function: y = 2 ^ Sin ^ 2 (2x)

The derivative of the function will be found as the derivative of a complex function.

y = 2 ^ (sin ^ 2 (2x)).

The function is indicative, the exponent is a complex function.

The derivative of a function is the same expression of a function, multiplied by the natural logarithm of the base and by the derivative of the exponent – the degree of the sine, its derivative and also by the derivative of the argument.

y ‘= 2 ^ (sin ^ 2 (2x)) * ln 2 * 2 * sin (2x) * cos (2x) * 2;

y ‘= sin 4x * ln 2 * 2 ^ (sin ^ 2 (2x) + 1).