Производни

[Гост]

Y= sin( cos [tex]x^{2}[/tex] (2x-1))
Y=2sin[tex]\sqrt{x}[/tex]-1
Y=[tex]\sqrt{\frac{x+1}{x}}[/tex]
Намерете производната на функцията:

[aifC]

1) [tex]y' = sin(cosx^{2}(2x-1))[/tex], Нека [tex]u = cos(x^{2})(2x-1) \Rightarrow cos(u)(-2xsin(x^{2}(2x-1)+2cos(x^{2})) = cos(cos(x^{2})(2x-1))(-2xsin(x^{2}(2x-1)+2cos(x^{2})) ;[/tex]

2) [tex]y' = 2sin\sqrt{x} -1 \Rightarrow sin(u) = cos(u),(u = \sqrt{x}); \sqrt{x} = \frac{1}{2\sqrt{x}} ; \Rightarrow \frac{cos(\sqrt{x})}{\sqrt{x}};[/tex]

3) [tex]y' = \sqrt{\frac{x+1}{x}} \Rightarrow u = \frac{x+1}{x}; \Rightarrow \frac{1}{2\sqrt{u}}, \frac{x+1}{x} = -\frac{1}{x^{2}};[/tex]
[tex]\frac{1}{\sqrt[2]{\frac{x+1}{x}}}(-\frac{1}{x^{2}}) = -\frac{1}{2x^{\frac{3}{2}}\sqrt{x+1}} ;[/tex]