derivative of In\sqrt[3]{6x+4}

Lösung

\frac{d}{d x} (I n 3 6 x + 4)

\frac{2 n I}{( 6 x + 4 ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} (I n 3 6 x + 4)

Behandle

n, I

als Konstante

Entferne die Konstante:

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

= I n \frac{d}{d x} (3 6 x + 4)

Wende die Kettenregel an:

\frac{1}{3 ( 6 x + 4 ) ^{\frac{2}{3}}} \frac{d}{d x} (6 x + 4)

= \frac{1}{3 ( 6 x + 4 ) ^{\frac{2}{3}}} \frac{d}{d x} (6 x + 4)

\frac{d}{d x} (6 x + 4) = 6

= I n \frac{1}{3 ( 6 x + 4 ) ^{\frac{2}{3}}} \cdot 6

Vereinfache

I n \frac{1}{3 ( 6 x + 4 ) ^{\frac{2}{3}}} \cdot 6 : \frac{2 n I}{( 6 x + 4 ) ^{\frac{2}{3}}}

= \frac{2 n I}{( 6 x + 4 ) ^{\frac{2}{3}}}

e x t re m e y = 1 - x^{2}

e x t re m e y = - x^{2} + 72 x - 458

e x t re m e f (x, y) = x^{2} + y^{2} + 4 x - 4 y

e x t re m e y = \frac{x + 5}{x ^{2} - 4}

e x t re m e f (x, y) = 4 - x^{4} + 2 x^{2} - y^{2}