d/(dt)((\sqrt[3]{t})/5)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende Radikal Regel an:

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

= \frac{1}{5} \frac{d}{d t} (t^{\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} t^{\frac{1}{3} - 1}

Vereinfache

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

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

\frac{\partial}{\partial x} (6 - (x^{2} + y^{2})^{\frac{1}{5}})

\frac{\partial}{\partial y} (x \cdot e^{x y + 1})

d er i v a t i v e y = x^{- 1}

y^{^{'}} = \frac{1}{x y}

t an g e n t f (x) = 8 x^{2} - 3, at x = 3