derivative of (6x-1(3x-5)^{-1})

解答

\frac{d}{d x} ((6 x - 1) (3 x - 5)^{- 1})

- \frac{27}{( 3 x - 5 ) ^{2}}

求解步骤

\frac{d}{d x} ((6 x - 1) (3 x - 5)^{- 1})

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 6 x - 1, g = (3 x - 5)^{- 1}

= \frac{d}{d x} (6 x - 1) (3 x - 5)^{- 1} + \frac{d}{d x} ((3 x - 5)^{- 1}) (6 x - 1)

\frac{d}{d x} (6 x - 1) = 6

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

= 6 (3 x - 5)^{- 1} + (- \frac{3}{( 3 x - 5 ) ^{2}}) (6 x - 1)

化简

6 (3 x - 5)^{- 1} + (- \frac{3}{( 3 x - 5 ) ^{2}}) (6 x - 1) : - \frac{27}{( 3 x - 5 ) ^{2}}

= - \frac{27}{( 3 x - 5 ) ^{2}}

t an g e n t f (x) = cos (\frac{π x}{2}), at x = 0.7

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