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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{3}{2 ( 1 - 2 x ) ^{\frac{5}{2}}} (- 2) : \frac{3}{( 1 - 2 x ) ^{\frac{5}{2}}}

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

Graph

Beliebte Beispiele

(\partial)/(\partial x)(x^{2/3}+y^{2/3})

\frac{\partial}{\partial x} (x^{\frac{2}{3}} + y^{\frac{2}{3}})

integral of 1/(sqrt(64+x^2))

\int \frac{1}{64 + x ^{2}} d x

f (x) = x cos (x)

derivative of ln(x+2x)

\frac{d}{d x} (ln (x) + 2 x)

taylor 1/(1+x^2),0

t a y l or \frac{1}{1 + x ^{2}}, 0