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Beliebt Rechnen >

derivative of \sqrt[7]{x}-4/x

Lösung

\frac{d}{d x} (7 x - \frac{4}{x})

Lösung

\frac{x ^{2} + 28 x ^{\frac{6}{7}}}{7 x ^{\frac{20}{7}}}

Schritte zur Lösung

\frac{d}{d x} (7 x - \frac{4}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (7 x) - \frac{d}{d x} (\frac{4}{x})

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

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

= \frac{1}{7 x ^{\frac{6}{7}}} - (- \frac{4}{x ^{2}})

Vereinfache

\frac{1}{7 x ^{\frac{6}{7}}} - (- \frac{4}{x ^{2}}) : \frac{x ^{2} + 28 x ^{\frac{6}{7}}}{7 x ^{\frac{20}{7}}}

= \frac{x ^{2} + 28 x ^{\frac{6}{7}}}{7 x ^{\frac{20}{7}}}

Graph

Beliebte Beispiele

derivative y=5sqrt(7e^{-2x)+6}

d er i v a t i v e y = 5 7 e^{- 2 x} + 6

limit as x approaches 0 of 2x-4

x \to 0 lim (2 x - 4)

steigung y=-5x^2

s l o p e y = - 5 x^{2}

derivative of (x^2+9^5)

\frac{d}{d x} ((x^{2} + 9)^{5})

derivative y=(2x)/(e^x)

d er i v a t i v e y = \frac{2 x}{e ^{x}}