derivative f(x)= 1/(5x+7)

解答

导数

f (x) = \frac{1}{5 x + 7}

- \frac{5}{( 5 x + 7 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{1}{5 x + 7})

使用指数法则:

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

= \frac{d}{d x} ((5 x + 7)^{- 1})

使用连锁律:

- \frac{1}{( 5 x + 7 ) ^{2}} \frac{d}{d x} (5 x + 7)

= - \frac{1}{( 5 x + 7 ) ^{2}} \frac{d}{d x} (5 x + 7)

\frac{d}{d x} (5 x + 7) = 5

= - \frac{1}{( 5 x + 7 ) ^{2}} \cdot 5

化简

- \frac{1}{( 5 x + 7 ) ^{2}} \cdot 5 : - \frac{5}{( 5 x + 7 ) ^{2}}

= - \frac{5}{( 5 x + 7 ) ^{2}}

t a y l or \frac{1}{( 1 + x )}

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