(\partial)/(\partial x)(2/(x-3))

Lösung

\frac{\partial}{\partial x} (\frac{2}{x - 3})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{2}{x - 3})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (x - 3) = 1

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

Vereinfache

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

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

d er i v a t i v e 2 arcsin (x^{4})

d er i v a t i v e \frac{5 x ^{4}}{e ^{x}}

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

d er i v a t i v e 6 e^{2 t}

a re a y = 3 x^{3}, y = 75 x