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Beliebt Rechnen >

derivative \sqrt[7]{t}+4sqrt(t^7)

Lösung

ableitung von

7 t + 4 t^{7}

Lösung

\frac{1 + 98 t ^{\frac{47}{14}}}{7 t ^{\frac{6}{7}}}

Schritte zur Lösung

\frac{d}{d t} (7 t + 4 t^{7})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d t} (7 t) + \frac{d}{d t} (4 t^{7})

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

\frac{d}{d t} (4 t^{7}) = 14 t^{\frac{5}{2}}

= \frac{1}{7 t ^{\frac{6}{7}}} + 14 t^{\frac{5}{2}}

Vereinfache

\frac{1}{7 t ^{\frac{6}{7}}} + 14 t^{\frac{5}{2}} : \frac{1 + 98 t ^{\frac{47}{14}}}{7 t ^{\frac{6}{7}}}

= \frac{1 + 98 t ^{\frac{47}{14}}}{7 t ^{\frac{6}{7}}}

Graph

Beliebte Beispiele

derivative of (4x+e^{-z^2}^3)

\frac{d}{d x} ((4 x + e^{- z^{2}})^{3})

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\int x x - 21 d x

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\int \frac{5}{x ^{2} + 18 x + 82} d x

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\int_{0}^{13} \frac{1}{x ^{\frac{1}{4}}} d x