de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative (55.9)/(t^2-0.31t+11.2)

Lösung

ableitung von

\frac{55.9}{t ^{2} - 0.31 t + 11.2}

Lösung

- \frac{55.9 ( 2 t - 0.31 )}{( t ^{2} - 0.31 t + 11.2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d t} (\frac{55.9}{t ^{2} - 0.31 t + 11.2})

Entferne die Konstante:

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

= 55.9 \frac{d}{d t} (\frac{1}{t ^{2} - 0.31 t + 11.2})

Wende Exponentenregel an:

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

= 55.9 \frac{d}{d t} ((t^{2} - 0.31 t + 11.2)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} \frac{d}{d t} (t^{2} - 0.31 t + 11.2)

= - \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} \frac{d}{d t} (t^{2} - 0.31 t + 11.2)

\frac{d}{d t} (t^{2} - 0.31 t + 11.2) = 2 t - 0.31

= 55.9 (- \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} (2 t - 0.31))

Vereinfache

55.9 (- \frac{1}{( t ^{2} - 0.31 t + 11.2 ) ^{2}} (2 t - 0.31)) : - \frac{55.9 ( 2 t - 0.31 )}{( t ^{2} - 0.31 t + 11.2 ) ^{2}}

= - \frac{55.9 ( 2 t - 0.31 )}{( t ^{2} - 0.31 t + 11.2 ) ^{2}}

Graph

Beliebte Beispiele

(dP)/(dt)=P(5-P)-4

\frac{d P}{d t} = P (5 - P) - 4

limit as x approaches 2 of x^3*2x^2

x \to 2 lim (x^{3} \cdot 2 x^{2})

(\partial)/(\partial x)(e^{-2x^2})

\frac{\partial}{\partial x} (e^{- 2 x^{2}})

8 y^{^{''}} - 32 y = 0

derivative f(x)=18sqrt(x)

d er i v a t i v e f (x) = 18 x