derivative (t-sqrt(t))/(t^{1/5)}

Lösung

ableitung von

\frac{t - t}{t ^{\frac{1}{5}}}

\frac{3 ( t - 1 )}{10 t ^{\frac{7}{10}}} + \frac{1}{2 t ^{\frac{1}{5}}}

Schritte zur Lösung

\frac{d}{d t} (\frac{t - t}{t ^{\frac{1}{5}}})

Vereinfache

\frac{t - t}{t ^{\frac{1}{5}}} : t^{\frac{3}{10}} (t - 1)

= \frac{d}{d t} (t^{\frac{3}{10}} (t - 1))

Wende die Produktregel an:

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

f = t^{\frac{3}{10}}, g = t - 1

= \frac{d}{d t} (t^{\frac{3}{10}}) (t - 1) + \frac{d}{d t} (t - 1) t^{\frac{3}{10}}

\frac{d}{d t} (t^{\frac{3}{10}}) = \frac{3}{10 t ^{\frac{7}{10}}}

\frac{d}{d t} (t - 1) = \frac{1}{2 t ^{\frac{1}{2}}}

= \frac{3}{10 t ^{\frac{7}{10}}} (t - 1) + \frac{1}{2 t ^{\frac{1}{2}}} t^{\frac{3}{10}}

Vereinfache

\frac{3}{10 t ^{\frac{7}{10}}} (t - 1) + \frac{1}{2 t ^{\frac{1}{2}}} t^{\frac{3}{10}} : \frac{3 ( t - 1 )}{10 t ^{\frac{7}{10}}} + \frac{1}{2 t ^{\frac{1}{5}}}

= \frac{3 ( t - 1 )}{10 t ^{\frac{7}{10}}} + \frac{1}{2 t ^{\frac{1}{5}}}

d er i v a t i v e y = x^{2 x + 1}

\int - \frac{5}{x} d x

\int - 6 x^{- 1} d x

y^{^{''}} + y^{^{'}} = 6 x

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