Pochodna

[Geldron]

mam problem z obliczeniem pochodnej

\(\displaystyle{ f(x)=ln(x+\sqrt{1+x^{2}})}\)

[jasny]

\(\displaystyle{ f'(x)=\frac{1+\frac{2x}{2\sqrt{1+x^2}}}{x+\sqrt{1+x^2}}= \frac{\frac{\sqrt{1+x^2}+x}{\sqrt{1+x^2}}}{x+\sqrt{1+x^2}}=\frac{1}{\sqrt{1+x^2}}}\)

[Lider_M]

\(\displaystyle{ \left(\ln g(x)\right)'=\frac{g'(x)}{g(x)}}\)

[setch]

oraz \(\displaystyle{ (\sqrt{f(x)})'=\frac{f'(x)}{2\sqrt{f(x)}}}\)