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Beliebt Rechnen >

derivative f(x)= 4/(sqrt((x^2+6x)^3))

Lösung

ableitung von

f (x) = \frac{4}{( x ^{2} + 6 x ) ^{3}}

Lösung

- \frac{6 ( x ^{2} + 6 x ) ^{2} ( 2 x + 6 )}{( ( x ^{2} + 6 x ) ^{3} ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} \frac{4}{( x ^{2} + 6 x ) ^{3}}

Entferne die Konstante:

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

= 4 \frac{d}{d x} \frac{1}{( x ^{2} + 6 x ) ^{3}}

Wende Exponentenregel an:

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

= 4 \frac{d}{d x} (((x^{2} + 6 x)^{3})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( ( x ^{2} + 6 x ) ^{3} ) ^{\frac{3}{2}}} \frac{d}{d x} ((x^{2} + 6 x)^{3})

= - \frac{1}{2 ( ( x ^{2} + 6 x ) ^{3} ) ^{\frac{3}{2}}} \frac{d}{d x} ((x^{2} + 6 x)^{3})

\frac{d}{d x} ((x^{2} + 6 x)^{3}) = 3 (x^{2} + 6 x)^{2} (2 x + 6)

= 4 - \frac{1}{2 ( ( x ^{2} + 6 x ) ^{3} ) ^{\frac{3}{2}}} \cdot 3 (x^{2} + 6 x)^{2} (2 x + 6)

Vereinfache

4 - \frac{1}{2 ( ( x ^{2} + 6 x ) ^{3} ) ^{\frac{3}{2}}} \cdot 3 (x^{2} + 6 x)^{2} (2 x + 6) : - \frac{6 ( x ^{2} + 6 x ) ^{2} ( 2 x + 6 )}{( ( x ^{2} + 6 x ) ^{3} ) ^{\frac{3}{2}}}

= - \frac{6 ( x ^{2} + 6 x ) ^{2} ( 2 x + 6 )}{( ( x ^{2} + 6 x ) ^{3} ) ^{\frac{3}{2}}}

Graph

Beliebte Beispiele

integral of ((ln(t))^4)/t

\int \frac{( ln ( t ) ) ^{4}}{t} d t

integral of 2x+c

\int 2 x + c d x

integral of sin(2pix)cos(5pix)

\int sin (2 π x) cos (5 π x) d x

derivative of ln(sqrt((x-3/(x-1))))

\frac{d}{d x} (ln (\frac{x - 3}{x - 1}))

x*(dy)/(dx)=sqrt(1-y^2)

x \cdot \frac{d y}{d x} = 1 - y^{2}