derivative f(x)= 1/(2x+3)

解答

导数

f (x) = \frac{1}{2 x + 3}

- \frac{2}{( 2 x + 3 ) ^{2}}

求解步骤

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

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

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

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

= - \frac{1}{( 2 x + 3 ) ^{2}} \cdot 2

化简

- \frac{1}{( 2 x + 3 ) ^{2}} \cdot 2 : - \frac{2}{( 2 x + 3 ) ^{2}}

= - \frac{2}{( 2 x + 3 ) ^{2}}

y^{^{'}} + \frac{2}{x} y = \frac{1}{x ^{2}}

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

y^{^{'}} = 2 (t + 1) y, y (0) = 1

y^{^{''}} + 2 \cdot y^{^{'}} + y = e^{- t}

n = 0 \sum \infty \frac{1}{2 ^{n} n !}