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Derivace funkce s tangens
Urči derivaci zadané funkce:
\( o(x)=\operatorname{tg} \frac{e^{x}}{\ln x} \)
\( \large o^{\prime}(x)=\frac{1}{\cos^2\frac{e^{x}}{\ln x}}\cdot\frac{e^{x}\ln(x)-\frac{e^{x}}{x}}{\ln^2x} \)
\( \large o^{\prime}(x)=\frac{1}{\cos^2\frac{e^{x}}{\ln x}}\cdot\frac{e^{x}\ln(x)+\frac{e^{x}}{x}}{\ln^2x} \)
\( \large o^{\prime}(x)=\frac{1}{\cos^2\frac{e^{x}}{\ln x}}\cdot\frac{e^{x}\ln(x)-\frac{e^{x}}{x}}{\ln x} \)
\( \large o^{\prime}(x)=\frac{1}{\sin^2\frac{e^{x}}{\ln x}}\cdot\frac{e^{x}\ln(x)-\frac{e^{x}}{x}}{\ln^2x} \)