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Beliebt Rechnen >

derivative f(t)= 1/((t^2+3t+1)^{5/2)}

Lösung

ableitung von

f (t) = \frac{1}{( t ^{2} + 3 t + 1 ) ^{\frac{5}{2}}}

Lösung

- \frac{5 ( 2 t + 3 )}{2 ( t ^{2} + 3 t + 1 ) ^{\frac{7}{2}}}

Schritte zur Lösung

\frac{d}{d t} (\frac{1}{( t ^{2} + 3 t + 1 ) ^{\frac{5}{2}}})

Wende Exponentenregel an:

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

= \frac{d}{d t} ((t^{2} + 3 t + 1)^{- \frac{5}{2}})

Wende die Kettenregel an:

- \frac{5}{2 ( t ^{2} + 3 t + 1 ) ^{\frac{7}{2}}} \frac{d}{d t} (t^{2} + 3 t + 1)

= - \frac{5}{2 ( t ^{2} + 3 t + 1 ) ^{\frac{7}{2}}} \frac{d}{d t} (t^{2} + 3 t + 1)

\frac{d}{d t} (t^{2} + 3 t + 1) = 2 t + 3

= - \frac{5}{2 ( t ^{2} + 3 t + 1 ) ^{\frac{7}{2}}} (2 t + 3)

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{5 ( 2 t + 3 )}{2 ( t ^{2} + 3 t + 1 ) ^{\frac{7}{2}}}

Graph

Beliebte Beispiele

integral of sqrt(1-e^x)

\int 1 - e^{x} d x

limit as x approaches-infinity of x^3-x

x \to - \infty lim (x^{3} - x)

limit as x approaches infinity of x^{-6}

x \to \infty lim (x^{- 6})

integral of-x*e^{3x}

\int - x \cdot e^{3 x} d x

integral of sqrt(x^2-y^2)

\int x^{2} - y^{2} d y