Още няколко производни на функции

[vandersexxx]

y =[tex]\frac{sinx - cos x}{sinx + cosx }[/tex]
y= [tex]arcsin\frac{2x^{3}}{1+x^{2} }[/tex]

y= [tex]x+\sqrt{1-x^{2}} arccosx[/tex]

y= [tex]ln (arccos \frac{1}{ \sqrt{x} })[/tex]

[seppen]

...

[vandersexxx]

Отваря ми някакъв друг сайт 100webspace.net

[martin123456]

1
[tex]y'=\frac{(\cos{x}-\sin{x})(\sin{x}+\cos{x})-(\sin{x}-\cos{x})(\cos{x}-\sin{x})}{(sinx + cosx)^2}[/tex]

[martin123456]

2
[tex]\frac{(\frac{2x^3}{1+x^2})'}{\sqrt{1-(\frac{2x^3}{1+x^2})^2}}=\frac{\frac{6x^2(1+x^2)-2x^32x}{(1+x^2)^2}}{\sqrt{1-(\frac{2x^3}{1+x^2})^2}}[/tex]

[martin123456]

3
[tex]y'=1+\frac{1}{2}\frac{-2x}{\sqrt{1-x^2}}arccosx-\sqrt{1-x^2}\frac{1}{\sqrt{1-x^2}}[/tex]

[martin123456]

4
[tex]\frac{(arccos \frac{1}{ \sqrt{x} })'}{arccos \frac{1}{ \sqrt{x} }}=\frac{\frac{1}{1-\frac{1}{x}}(x^{-\frac{1}{2}})'}{arccos \frac{1}{ \sqrt{x} }}=\frac{\frac{1}{1-\frac{1}{x}}(-\frac{1}{2})x^{-\frac{3}{2}}}{arccos \frac{1}{ \sqrt{x} }}[/tex]

[vandersexxx]

черпилката от мен