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Beliebt Rechnen >

derivative 9x^{4/3}-2/3 x^{3/2}+x^2-3x+1

Lösung

ableitung von

9 x^{\frac{4}{3}} - \frac{2}{3} x^{\frac{3}{2}} + x^{2} - 3 x + 1

Lösung

2 x + 12 x^{\frac{1}{3}} - x^{\frac{1}{2}} - 3

Schritte zur Lösung

\frac{d}{d x} (9 x^{\frac{4}{3}} - \frac{2}{3} x^{\frac{3}{2}} + x^{2} - 3 x + 1)

Vereinfache

9 x^{\frac{4}{3}} - \frac{2}{3} x^{\frac{3}{2}} + x^{2} - 3 x + 1 : 9 x^{\frac{4}{3}} - \frac{2 x ^{\frac{3}{2}}}{3} + x^{2} - 3 x + 1

= \frac{d}{d x} (9 x^{\frac{4}{3}} - \frac{2 x ^{\frac{3}{2}}}{3} + x^{2} - 3 x + 1)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (9 x^{\frac{4}{3}}) - \frac{d}{d x} (\frac{2 x ^{\frac{3}{2}}}{3}) + \frac{d}{d x} (x^{2}) - \frac{d}{d x} (3 x) + \frac{d}{d x} (1)

\frac{d}{d x} (9 x^{\frac{4}{3}}) = 12 x^{\frac{1}{3}}

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (3 x) = 3

\frac{d}{d x} (1) = 0

= 12 x^{\frac{1}{3}} - x^{\frac{1}{2}} + 2 x - 3 + 0

Vereinfache

= 2 x + 12 x^{\frac{1}{3}} - x^{\frac{1}{2}} - 3

Graph

Beliebte Beispiele

limit as x approaches-211 of (5-x)^{2/3}

x \to - 211 lim ((5 - x)^{\frac{2}{3}})

integral from 0 to h of (L^2)/(h^2)x^2

\int_{0}^{h} \frac{L ^{2}}{h ^{2}} x^{2} d x

(dy)/(dx)=((x^2y^2))/(1+x)

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

derivative of ,x^2

\frac{d}{d x} (, x^{2})

integral of-x^{1/3}

\int - x^{\frac{1}{3}} d x