Вычислить производную сложной функции. у=√sin(2x²-π)                  ͞8

1/2*cos(x^2-П/8)*4x/sqrt(sin(2x^2-П/2))

[latex]y'=(\sqrt {sin {\frac {2x^2-\pi}{8}}})'= \frac{(sin {\frac {2x^2-\pi}{8}})'} {2\sqrt {sin {\frac {2x^2-\pi}{8}}}}= \frac {cos {\frac {2x^2-\pi}{8}}} {2\sqrt {sin {\frac {2x^2-\pi}{8}}}} *(\frac {2x^2-\pi}{8})'}= [/latex] [latex]=\frac {cos {\frac {2x^2-\pi}{8}}} {2\sqrt {sin {\frac {2x^2-\pi}{8}}}} *(\frac {1}{8})}*(2x^2-\pi)'= =\frac {cos {\frac {2x^2-\pi}{8}}} {2\sqrt {sin {\frac {2x^2-\pi}{8}}}} *(\frac {1}{8})}*(4x-0)=[/latex] [latex]=\frac {x cos {\frac {2x^2-\pi}{8}}} {4\sqrt {sin {\frac {2x^2-\pi}{8}}}}[/latex]