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Derivace funkce f(x)=√(x²-1)
Urči derivaci funkce f(x)=\sqrt{x^{2}-1}, když víš, že f^{\prime}(\sqrt{5}).
f^{\prime}(\sqrt{5})=\lim _{x \rightarrow \sqrt{5}} \frac{\sqrt{x^{2}-1}-2}{x-\sqrt{5}}=\frac{5}{2}
f^{\prime}(\sqrt{5})=\lim _{x \rightarrow \sqrt{5}} \frac{\sqrt{x^{2}-1}-2}{x-\sqrt{5}}=\frac{\sqrt{5}}{2}
f^{\prime}(\sqrt{5})=\lim _{x \rightarrow \sqrt{5}} \frac{\sqrt{x^{2}-1}-3}{x-\sqrt{5}}=\frac{\sqrt{5}}{2}
f^{\prime}(\sqrt{5})=\lim _{x \rightarrow \sqrt{5}} \frac{\sqrt{x^{2}-1}-2}{x-\sqrt{5}}=\frac{\sqrt{5}}{3}