derivative of (14+5x-3x^2^{3/4})

Lösung

\frac{d}{d x} ((14 + 5 x - 3 x^{2})^{\frac{3}{4}})

\frac{3 ( - 6 x + 5 )}{4 ( 14 + 5 x - 3 x ^{2} ) ^{\frac{1}{4}}}

Schritte zur Lösung

\frac{d}{d x} ((14 + 5 x - 3 x^{2})^{\frac{3}{4}})

Wende die Kettenregel an:

\frac{3}{4 ( 14 + 5 x - 3 x ^{2} ) ^{\frac{1}{4}}} \frac{d}{d x} (14 + 5 x - 3 x^{2})

= \frac{3}{4 ( 14 + 5 x - 3 x ^{2} ) ^{\frac{1}{4}}} \frac{d}{d x} (14 + 5 x - 3 x^{2})

\frac{d}{d x} (14 + 5 x - 3 x^{2}) = - 6 x + 5

= \frac{3}{4 ( 14 + 5 x - 3 x ^{2} ) ^{\frac{1}{4}}} (- 6 x + 5)

Multipliziere Brüche:

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

= \frac{3 ( - 6 x + 5 )}{4 ( 14 + 5 x - 3 x ^{2} ) ^{\frac{1}{4}}}

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