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Beliebt Rechnen >

derivative f(x)=x^{19/9}+x^{10/9}

Lösung

ableitung von

f (x) = x^{\frac{19}{9}} + x^{\frac{10}{9}}

Lösung

\frac{19 x ^{\frac{10}{9}} + 10 x ^{\frac{1}{9}}}{9}

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{19}{9}} + x^{\frac{10}{9}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{\frac{19}{9}}) + \frac{d}{d x} (x^{\frac{10}{9}})

\frac{d}{d x} (x^{\frac{19}{9}}) = \frac{19 x ^{\frac{10}{9}}}{9}

\frac{d}{d x} (x^{\frac{10}{9}}) = \frac{10 x ^{\frac{1}{9}}}{9}

= \frac{19 x ^{\frac{10}{9}}}{9} + \frac{10 x ^{\frac{1}{9}}}{9}

Wende Regel an

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{19 x ^{\frac{10}{9}} + 10 x ^{\frac{1}{9}}}{9}

Graph

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