derivada de ((2+e^x/3)^9)

Solución

\frac{d}{d x} ((\frac{2 + e ^{x}}{3})^{9})

\frac{e ^{x} ( e ^{x} + 2 ) ^{8}}{2187}

Pasos de solución

\frac{d}{d x} ((\frac{2 + e ^{x}}{3})^{9})

Aplicar la regla de la cadena:

9 (\frac{2 + e ^{x}}{3})^{8} \frac{d}{d x} (\frac{2 + e ^{x}}{3})

= 9 (\frac{2 + e ^{x}}{3})^{8} \frac{d}{d x} (\frac{2 + e ^{x}}{3})

\frac{d}{d x} (\frac{2 + e ^{x}}{3}) = \frac{1}{3} e^{x}

= 9 (\frac{2 + e ^{x}}{3})^{8} \frac{1}{3} e^{x}

Simplificar

9 (\frac{2 + e ^{x}}{3})^{8} \frac{1}{3} e^{x} : \frac{e ^{x} ( e ^{x} + 2 ) ^{8}}{2187}

= \frac{e ^{x} ( e ^{x} + 2 ) ^{8}}{2187}

\int \frac{e ^{2 x}}{e ^{5 - x}} d x

\int \frac{40}{1 - cos ( 8 x )} d x

x \to \infty lim (67)

\int_{- 2}^{x} \frac{x + 2}{3} d x

\frac{3}{x ^{9}}