derivative f(x)=(2x-1)(6x-6)^{-1}

Lösung

ableitung von

f (x) = (2 x - 1) (6 x - 6)^{- 1}

- \frac{1}{6 ( x - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} ((2 x - 1) (6 x - 6)^{- 1})

Wende die Produktregel an:

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

f = 2 x - 1, g = (6 x - 6)^{- 1}

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

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

\frac{d}{d x} ((6 x - 6)^{- 1}) = - \frac{1}{6 ( x - 1 ) ^{2}}

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

Vereinfache

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

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

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

(tan (y)) d x - (cot (x)) d y = 0

\int \frac{x - 9}{( x + 5 ) ( x - 2 )} d x

\frac{\partial}{\partial x} (2 y - x^{2} + 2)

t an g e n t 2 e^{x - 2}