derivative g(x)= 1/(5x^2+3x)

解答

导数

g (x) = \frac{1}{5 x ^{2} + 3 x}

- \frac{10 x + 3}{( 5 x ^{2} + 3 x ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{1}{5 x ^{2} + 3 x})

使用指数法则:

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

= \frac{d}{d x} ((5 x^{2} + 3 x)^{- 1})

使用连锁律:

- \frac{1}{( 5 x ^{2} + 3 x ) ^{2}} \frac{d}{d x} (5 x^{2} + 3 x)

= - \frac{1}{( 5 x ^{2} + 3 x ) ^{2}} \frac{d}{d x} (5 x^{2} + 3 x)

\frac{d}{d x} (5 x^{2} + 3 x) = 10 x + 3

= - \frac{1}{( 5 x ^{2} + 3 x ) ^{2}} (10 x + 3)

化简

- \frac{1}{( 5 x ^{2} + 3 x ) ^{2}} (10 x + 3) : - \frac{10 x + 3}{( 5 x ^{2} + 3 x ) ^{2}}

= - \frac{10 x + 3}{( 5 x ^{2} + 3 x ) ^{2}}

x \to \infty lim (x^{- 7})

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