derivative f(x)= 1/(sqrt(x-1))

Lösung

ableitung von

f (x) = \frac{1}{x - 1}

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

\frac{d}{d x} (x (3 x - 9)^{3})

\int_{0}^{5} \frac{2 x - 1}{x + 1} d x

\int_{0}^{2} x e^{- x^{2}} d x

\int ∣ x ∣ d x

\frac{\partial}{\partial x} (a^{x} - b^{x})