(\partial)/(\partial x)(1/(1-bx))

Lösung

\frac{\partial}{\partial x} (\frac{1}{1 - b x})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{1 - b x})

Behandle

b

als Konstante

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} ((2 x - 7)^{4} (x^{2} + x + 1)^{5})

y^{^{''}} + y^{^{'}} - 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1

x \to \infty lim (- \frac{sin ^{2} ( x ) + 2}{2 x - 5})

\frac{\partial}{\partial x} (sin (3 x) cos (6 y))

\frac{d}{d x} (x^{2} + 8 x)