Pochodne

[wojtek30paz]

Oblicz pochodna F(x)=arc cos (\sqrt{cosx})

[Galen]

\(f(x}=arc cos (\sqrt{cosx})\)
\(f'(x)= \frac{-1}{ \sqrt{1- (\sqrt{cosx})^2 } } \cdot \frac{1}{2 \sqrt{cosx} } \cdot (-sinx)= \frac{sinx}{ \sqrt{1-cosx} \cdot 2 \sqrt{cosx} }= \frac{sinx}{2 \sqrt{cosx-cos^2x} }\)

[wojtek30paz]

pochodna \(arc sin (\frac{2x-1}{ \sqrt{5} } )\)

[Galen]

\(f'(x)=[arc sin(\frac{1}{\sqrt{5}})\cdot (2x-1)]'= \frac{2}{ \sqrt{5}\cdot \sqrt{1- \frac{1}{5} \cdot (2x-1)^2 } }\)

http://forum.zadania.info/viewtopic.php?f=29&t=12617
Punkty:8 i 12

[Crazy Driver]

http://www.wolframalpha.com/