(\partial)/(\partial x)((ln(1+e^{(x)}))^2)

解答

\frac{\partial}{\partial x} ((ln (1 + e^{(x)}))^{2})

\frac{2 e ^{x} ln ( 1 + e ^{x} )}{1 + e ^{x}}

求解步骤

\frac{\partial}{\partial x} ((ln (1 + e^{(x)}))^{2})

使用连锁律:

2 ln (1 + e^{x}) \frac{\partial}{\partial x} (ln (1 + e^{x}))

= 2 ln (1 + e^{x}) \frac{\partial}{\partial x} (ln (1 + e^{x}))

\frac{\partial}{\partial x} (ln (1 + e^{x})) = \frac{e ^{x}}{1 + e ^{x}}

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

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

t \to 0 lim (\frac{2 e ^{t} - 2}{t})

\int 2 + 2 cos (x) d x

\int \frac{1}{3 - 4 x - x ^{2}} d x

d y = (x - 2 y cot (2 x)) d x

d er i v a t i v e x (8 x + 5)^{4}