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Beliebt Rechnen >

derivative 1/((2x^3+3x+5)^{3/4)}

Lösung

ableitung von

\frac{1}{( 2 x ^{3} + 3 x + 5 ) ^{\frac{3}{4}}}

Lösung

- \frac{3 ( 6 x ^{2} + 3 )}{4 ( 2 x ^{3} + 3 x + 5 ) ^{\frac{7}{4}}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

- \frac{3}{4 ( 2 x ^{3} + 3 x + 5 ) ^{\frac{7}{4}}} \frac{d}{d x} (2 x^{3} + 3 x + 5)

= - \frac{3}{4 ( 2 x ^{3} + 3 x + 5 ) ^{\frac{7}{4}}} \frac{d}{d x} (2 x^{3} + 3 x + 5)

\frac{d}{d x} (2 x^{3} + 3 x + 5) = 6 x^{2} + 3

= - \frac{3}{4 ( 2 x ^{3} + 3 x + 5 ) ^{\frac{7}{4}}} (6 x^{2} + 3)

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{3 ( 6 x ^{2} + 3 )}{4 ( 2 x ^{3} + 3 x + 5 ) ^{\frac{7}{4}}}

Graph

Beliebte Beispiele

integral from 1 to e of (ln(x))^2

\int_{1}^{e} (ln (x))^{2} d x

integral of (x^2)/(x^3+1)

\int \frac{x ^{2}}{x ^{3} + 1} d x

(dy}{dx}=\frac{(-xe^{-x^2}))/y

\frac{d y}{d x} = \frac{( - x e ^{- x^{2}} )}{y}

integral of 8x^2cos(2x)

\int 8 x^{2} cos (2 x) d x

integral of (x^2+1)^3*x

\int (x^{2} + 1)^{3} \cdot x d x