derivative of 1/(ax+b)

Lösung

\frac{d}{d x} (\frac{1}{a x + b})

- \frac{a}{( a x + b ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{a x + b})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((a x + b)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( a x + b ) ^{2}} \frac{d}{d x} (a x + b)

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

\frac{d}{d x} (a x + b) = a

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

Vereinfache

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

= - \frac{a}{( a x + b ) ^{2}}

\int - 2 sin^{3} (x) cos (x) d x

\int \frac{5 t - 2}{t + 1} d t

\frac{d}{d x} (\frac{x}{12} + 1)

\int_{1}^{2} 2 x^{3} - 4 d x

\frac{\partial}{\partial x} (\frac{5 y ^{2}}{x})