derivative of 2x^{1/4}(x^3-11)

Lösung

\frac{d}{d x} (2 x^{\frac{1}{4}} (x^{3} - 11))

\frac{13 x ^{3} - 11}{2 x ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (2 x^{\frac{1}{4}} (x^{3} - 11))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (x^{\frac{1}{4}} (x^{3} - 11))

Wende die Produktregel an:

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

f = x^{\frac{1}{4}}, g = x^{3} - 11

= 2 (\frac{d}{d x} (x^{\frac{1}{4}}) (x^{3} - 11) + \frac{d}{d x} (x^{3} - 11) x^{\frac{1}{4}})

\frac{d}{d x} (x^{\frac{1}{4}}) = \frac{1}{4 x ^{\frac{3}{4}}}

\frac{d}{d x} (x^{3} - 11) = 3 x^{2}

= 2 (\frac{1}{4 x ^{\frac{3}{4}}} (x^{3} - 11) + 3 x^{2} x^{\frac{1}{4}})

Vereinfache

2 (\frac{1}{4 x ^{\frac{3}{4}}} (x^{3} - 11) + 3 x^{2} x^{\frac{1}{4}}) : \frac{13 x ^{3} - 11}{2 x ^{\frac{3}{4}}}

= \frac{13 x ^{3} - 11}{2 x ^{\frac{3}{4}}}

t an g e n t f (x) = 5 x^{2} + 4

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