derivative y=(5t-1)(2t-3)^{-1}

解答

导数

y = (5 t - 1) (2 t - 3)^{- 1}

- \frac{13}{( 2 t - 3 ) ^{2}}

求解步骤

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

使用微分乘法定则:

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

f = 5 t - 1, g = (2 t - 3)^{- 1}

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

\frac{d}{d t} (5 t - 1) = 5

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

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

化简

5 (2 t - 3)^{- 1} + (- \frac{2}{( 2 t - 3 ) ^{2}}) (5 t - 1) : - \frac{13}{( 2 t - 3 ) ^{2}}

= - \frac{13}{( 2 t - 3 ) ^{2}}

n = 1 \sum \infty \frac{2}{n ( n + 1 )}

a re a y = 7 x, y = 44 - x^{2}

n = 2 \sum \infty \frac{1}{ln ( n )}

d er i v a t i v e csc^{2} (x)

t an g e n t f (x) = 3 x^{2} + 5 x - 4, at x = - 0.6667