derivative (t-sqrt(t))/(t^{1/7)}

Lösung

ableitung von

\frac{t - t}{t ^{\frac{1}{7}}}

\frac{5 ( t - 1 )}{14 t ^{\frac{9}{14}}} + \frac{1}{2 t ^{\frac{1}{7}}}

Schritte zur Lösung

\frac{d}{d t} (\frac{t - t}{t ^{\frac{1}{7}}})

Vereinfache

\frac{t - t}{t ^{\frac{1}{7}}} : t^{\frac{5}{14}} (t - 1)

= \frac{d}{d t} (t^{\frac{5}{14}} (t - 1))

Wende die Produktregel an:

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

f = t^{\frac{5}{14}}, g = t - 1

= \frac{d}{d t} (t^{\frac{5}{14}}) (t - 1) + \frac{d}{d t} (t - 1) t^{\frac{5}{14}}

\frac{d}{d t} (t^{\frac{5}{14}}) = \frac{5}{14 t ^{\frac{9}{14}}}

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

= \frac{5}{14 t ^{\frac{9}{14}}} (t - 1) + \frac{1}{2 t ^{\frac{1}{2}}} t^{\frac{5}{14}}

Vereinfache

\frac{5}{14 t ^{\frac{9}{14}}} (t - 1) + \frac{1}{2 t ^{\frac{1}{2}}} t^{\frac{5}{14}} : \frac{5 ( t - 1 )}{14 t ^{\frac{9}{14}}} + \frac{1}{2 t ^{\frac{1}{7}}}

= \frac{5 ( t - 1 )}{14 t ^{\frac{9}{14}}} + \frac{1}{2 t ^{\frac{1}{7}}}

\frac{d}{d x} (x sin (y - z))

d er i v a t i v e y = (\frac{3 x ^{2}}{2 x + 4})^{3}

in v erse l a pl a ce \frac{5}{s ( s ^{2} + 5 ^{2} )}

l a pl a ce t r an s f or m f (t) = 2 (1 - e^{- 5 t})

\frac{d}{d x} (ln^{2} (2) \cdot 2^{x})