de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative f(x)= 5/((2x-3)^4)

Lösung

ableitung von

f (x) = \frac{5}{( 2 x - 3 ) ^{4}}

Lösung

- \frac{40}{( 2 x - 3 ) ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{5}{( 2 x - 3 ) ^{4}})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (\frac{1}{( 2 x - 3 ) ^{4}})

Wende Exponentenregel an:

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

= 5 \frac{d}{d x} ((2 x - 3)^{- 4})

Wende die Kettenregel an:

- \frac{4}{( 2 x - 3 ) ^{5}} \frac{d}{d x} (2 x - 3)

= - \frac{4}{( 2 x - 3 ) ^{5}} \frac{d}{d x} (2 x - 3)

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

= 5 (- \frac{4}{( 2 x - 3 ) ^{5}} \cdot 2)

Vereinfache

5 (- \frac{4}{( 2 x - 3 ) ^{5}} \cdot 2) : - \frac{40}{( 2 x - 3 ) ^{5}}

= - \frac{40}{( 2 x - 3 ) ^{5}}

Graph

Beliebte Beispiele

derivative of sin(xln(5x))

\frac{d}{d x} (sin (x) ln (5 x))

derivative e^{19}

d er i v a t i v e e^{19}

(dy)/(dx)=e^4x+7y

\frac{d y}{d x} = e^{4} x + 7 y

integral of xsqrt(3x^2-6)

\int x 3 x^{2} - 6 d x

limit as x approaches 2 of (2x^2-5x+2)/(x^3-2x^2)

x \to 2 lim (\frac{2 x ^{2} - 5 x + 2}{x ^{3} - 2 x ^{2}})