derivative \sqrt[7]{t}+6sqrt(t^7)

Lösung

ableitung von

7 t + 6 t^{7}

\frac{1 + 147 t ^{\frac{47}{14}}}{7 t ^{\frac{6}{7}}}

Schritte zur Lösung

\frac{d}{d t} (7 t + 6 t^{7})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (7 t) + \frac{d}{d t} (6 t^{7})

\frac{d}{d t} (7 t) = \frac{1}{7 t ^{\frac{6}{7}}}

\frac{d}{d t} (6 t^{7}) = 21 t^{\frac{5}{2}}

= \frac{1}{7 t ^{\frac{6}{7}}} + 21 t^{\frac{5}{2}}

Vereinfache

\frac{1}{7 t ^{\frac{6}{7}}} + 21 t^{\frac{5}{2}} : \frac{1 + 147 t ^{\frac{47}{14}}}{7 t ^{\frac{6}{7}}}

= \frac{1 + 147 t ^{\frac{47}{14}}}{7 t ^{\frac{6}{7}}}

a re a y = 5 x - x^{2}, y = - x

\frac{\partial}{\partial x} (3 y cos (x))

in v erse l a pl a ce \frac{1}{s [ 5 + s ]}

y^{^{''}} - 12 y^{^{'}} + 36 y = 0

\frac{d ^{2}}{d x ^{2}} (cos (x))