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Beliebt Rechnen >

derivative of 1/(\sqrt[4]{x^5})

Lösung

\frac{d}{d x} (\frac{1}{4 x ^{5}})

Lösung

- \frac{5}{4 x ^{\frac{9}{4}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{4 x ^{5}})

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

= - \frac{1}{4 ( x ^{5} ) ^{\frac{5}{4}}} \cdot 5 x^{4}

Vereinfache

- \frac{1}{4 ( x ^{5} ) ^{\frac{5}{4}}} \cdot 5 x^{4} : - \frac{5}{4 x ^{\frac{9}{4}}}

= - \frac{5}{4 x ^{\frac{9}{4}}}

Graph

Beliebte Beispiele

integral from 0 to 6 of sqrt(36-x^2)

\int_{0}^{6} 36 - x^{2} d x

integral of (33)/(33+e^x)

\int \frac{33}{33 + e ^{x}} d x

integral of ((x^2-1))/x

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

derivative of ln(x^2+1-e^{x/2}cos(pix))

\frac{d}{d x} (ln (x^{2} + 1) - e^{\frac{x}{2}} cos (π x))

integral of (4x+5)/(x^2+4x+2)

\int \frac{4 x + 5}{x ^{2} + 4 x + 2} d x