derivative of ln(e^x+3)

解答

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

\frac{e ^{x}}{e ^{x} + 3}

求解步骤

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

使用连锁律:

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

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

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

= \frac{1}{e ^{x} + 3} e^{x}

化简

\frac{1}{e ^{x} + 3} e^{x} : \frac{e ^{x}}{e ^{x} + 3}

= \frac{e ^{x}}{e ^{x} + 3}

\int tan (9 x) sec^{\frac{5}{4}} (9 x) d x

t \to - 3 lim (\frac{t - 2}{t + 5})

\int \frac{3 \cdot 2 ^{x} - 2 \cdot 3 ^{x}}{2 x} d x

\int \frac{x ^{4} - x ^{3}}{x ^{5}} d x

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