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Beliebt Rechnen >

derivative of (\sqrt[3]{x}/5)

Lösung

\frac{d}{d x} (\frac{3 x}{5})

Lösung

\frac{1}{15 x ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x}{5})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Radikal Regel an:

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

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

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{5} \cdot \frac{1}{3} x^{\frac{1}{3} - 1}

Vereinfache

\frac{1}{5} \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{1}{15 x ^{\frac{2}{3}}}

= \frac{1}{15 x ^{\frac{2}{3}}}

Graph

Beliebte Beispiele

tangent f(x)=3ln(x^5),\at (15)/e

t an g e n t f (x) = 3 ln (x^{5}), at \frac{15}{e}

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

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

integral of (x+1)sin(5x)

\int (x + 1) sin (5 x) d x

(dy)/(dx)=(cos(20x))/(e^{20y)},y(0)=2

\frac{d y}{d x} = \frac{cos ( 20 x )}{e ^{20 y}}, y (0) = 2

integral of x^2cos(x

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