derivative of (3x+1/(x^{2/3)})

Lösung

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

\frac{3 x - 2}{3 x ^{\frac{5}{3}}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{3 x ^{\frac{2}{3}} - \frac{2}{3 x ^{\frac{1}{3}}} ( 3 x + 1 )}{( x ^{\frac{2}{3}} ) ^{2}} : \frac{3 x - 2}{3 x ^{\frac{5}{3}}}

= \frac{3 x - 2}{3 x ^{\frac{5}{3}}}

\int e^{\frac{- 1}{x}} d x

d er i v a t i v e 10 \cdot 2^{- 0.274 x}

d er i v a t i v e \frac{2 x}{7 - tan ( x )}

a re a f (x) = 4 - x, x = - 2, x = 3, y = 0

ma c l a u r in 11 e^{- x}