derivative (4x+4)/(3x^{2/3)}

Lösung

ableitung von

\frac{4 x + 4}{3 x ^{\frac{2}{3}}}

\frac{4 x - 8}{9 x ^{\frac{5}{3}}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

= \frac{1}{3} \cdot \frac{4 x ^{\frac{2}{3}} - \frac{2}{3 x ^{\frac{1}{3}}} ( 4 x + 4 )}{( x ^{\frac{2}{3}} ) ^{2}}

Vereinfache

\frac{1}{3} \cdot \frac{4 x ^{\frac{2}{3}} - \frac{2}{3 x ^{\frac{1}{3}}} ( 4 x + 4 )}{( x ^{\frac{2}{3}} ) ^{2}} : \frac{4 x - 8}{9 x ^{\frac{5}{3}}}

= \frac{4 x - 8}{9 x ^{\frac{5}{3}}}

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

l a pl a ce t r an s f or m 3 sin (2)

s l o p e 3 x^{3} + 5 y^{3} = 1

y^{^{'}} - e^{7 x + y} = 0

x \to 2 lim (3 x + a)