derivative of In\sqrt[5]{x}

Lösung

\frac{d}{d x} (I n 5 x)

\frac{n I}{5 x ^{\frac{4}{5}}}

Schritte zur Lösung

\frac{d}{d x} (I n 5 x)

Behandle

n, I

als Konstante

Entferne die Konstante:

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

= I n \frac{d}{d x} (5 x)

Wende Radikal Regel an:

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

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

Wende die Potenzregel an:

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

= I n \frac{1}{5} x^{\frac{1}{5} - 1}

Vereinfache

I n \frac{1}{5} x^{\frac{1}{5} - 1} : \frac{n I}{5 x ^{\frac{4}{5}}}

= \frac{n I}{5 x ^{\frac{4}{5}}}

e x t re m e e^{x^{2} - 7 x - 1}

e x t re m e f (x, y) = - x^{2} + y^{2}

e x t re m e q (x, z) = 3 x + 9 x z

e x t re m e f (x, y) = 2 x^{3} + y^{2} - 24 x

e x t re m e f (θ) = - 5 cos (\frac{3}{4} θ - 6) - 2