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Beliebt Rechnen >

derivative of (1+\sqrt[3]{x}^3)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

limit as x approaches 1 of x^{17}-x+3

x \to 1 lim (x^{17} - x + 3)

derivative of 3x^2+2y^4

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

d/(dy)(e^{-xy})

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

integral of (3-x^2)3

\int (3 - x^{2}) 3 d x

(dy)/(dx)=(1/(sec^2(y)))

\frac{d y}{d x} = (\frac{1}{sec ^{2} ( y )})