Question

Найти производную данной функции и упростить ее:
y=(sin^2x)/(sinx^2)

Answer 1

$y= frac{sin^2x}{sin x^2}$

$y'= frac{(sin^2x)'sin x^2-sin^2x(sin x^2)'}{sin^2x^2} = frac{(2sin xcos x)sin x^2-sin^2x(2xcos x^2)}{sin^2x^2} = \ =frac{2sin xcos xsin x^2-2xsin^2xcos x^2}{sin^2x^2} = frac{2sin x(cos xsin x^2-xsin xcos x^2)}{sin^2x^2}$