derivative of (\sqrt[7]{x}/6)

Lösung

\frac{d}{d x} (\frac{7 x}{6})

\frac{1}{42 x ^{\frac{6}{7}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 x}{6})

Entferne die Konstante:

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

= \frac{1}{6} \frac{d}{d x} (7 x)

Wende Radikal Regel an:

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

= \frac{1}{6} \frac{d}{d x} (x^{\frac{1}{7}})

Wende die Potenzregel an:

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

= \frac{1}{6} \cdot \frac{1}{7} x^{\frac{1}{7} - 1}

Vereinfache

\frac{1}{6} \cdot \frac{1}{7} x^{\frac{1}{7} - 1} : \frac{1}{42 x ^{\frac{6}{7}}}

= \frac{1}{42 x ^{\frac{6}{7}}}

\frac{\partial}{\partial x} (6 e^{x^{5} y^{3}})

\int 10 x^{3} y d y

d er i v a t i v e y = \frac{( x )}{x ^{2} + 1}

t an g e n t 5 x

s l o p e f (x) = x^{4} - 17 x^{2} + 16