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}}

\frac{d}{d x} (x^{2} - 4 x - 3)

d er i v a t i v e \frac{x ^{2} + 2 x}{( x + 1 ) ^{2}}

\frac{\partial}{\partial h} (2 π r^{2} + 2 π r h)

a re a f (x) = x^{5} + 2, g (x) = x + 2

d er i v a t i v e y = e^{x} ln (x)