derivative of 1/(x^2-3x)

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int e^{- a \cdot x^{2}} d x

f (x) = 5 cos (x)

\frac{d}{d x} (\frac{0.25 e ^{x}}{1 - 0.75 e ^{x}})

y^{^{''}} - 2 y^{^{'}} - 3 y = - 6 cos (t) - 9 sin (t)

\int 3 x^{2} + 5 x^{\frac{1}{3}} + 7 sin (x) d x