Question

Найти производную 3^х^х

Answer 1

$\frac{d}{dx} (3 {}^{x {}^{x} } ) \\ \frac{d}{dg} (3 {}^{g} ) \times \frac{d}{dx} (x {}^{x} ) \\ ln(3) \times 3 {}^{g} \times e {}^{ ln(x) x} \times ( \frac{1}{x} \times x + ln(x) ) \\ ln(3) \times 3 {}^{x {}^{x} } \times e {}^{ ln(x) } \times ( \frac{1}{x} \times x + ln(x) ) \\ ln(3) \times 3 {}^{x {}^{x} } \times x {}^{x} + ln(3) \times 3 {}^{x {}^{x} } \times x {}^{x} \times ln(x)$

Answer 2

Ответ:

$y=3^{x^x}\\\\lny=x^xln3\\\\\dfrac{y'}{y} =x^x(lnx+1)ln3\\\\y'=3^{x^x}x^x(lnx+1)ln3$

Пошаговое объяснение: