derivative y=x^{2/5}(x+3)

Lösung

ableitung von

y = x^{\frac{2}{5}} (x + 3)

\frac{7 x + 6}{5 x ^{\frac{3}{5}}}

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{2}{5}} (x + 3))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{2}{5}}, g = x + 3

= \frac{d}{d x} (x^{\frac{2}{5}}) (x + 3) + \frac{d}{d x} (x + 3) x^{\frac{2}{5}}

\frac{d}{d x} (x^{\frac{2}{5}}) = \frac{2}{5 x ^{\frac{3}{5}}}

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

= \frac{2}{5 x ^{\frac{3}{5}}} (x + 3) + 1 \cdot x^{\frac{2}{5}}

Vereinfache

\frac{2}{5 x ^{\frac{3}{5}}} (x + 3) + 1 \cdot x^{\frac{2}{5}} : \frac{7 x + 6}{5 x ^{\frac{3}{5}}}

= \frac{7 x + 6}{5 x ^{\frac{3}{5}}}

\frac{d}{d x} (\frac{x ^{3} - 4}{x - 1})

\int \frac{3 x - 2}{x + 1} d x

x \to - 3 lim (∣ - x - 1 ∣)

\int \frac{1}{( x - 3 ) ( x - 1 )} d x

d er i v a t i v e \frac{6}{5} - \frac{6}{5} e^{- 20 t}