derivative f(x)=6sqrt(6x^{10)+7x^6}

Lösung

ableitung von

f (x) = 6 6 x^{10} + 7 x^{6}

\frac{3 ( 60 x ^{9} + 42 x ^{5} )}{x ^{6} 6 x ^{4} + 7}

Schritte zur Lösung

\frac{d}{d x} (6 6 x^{10} + 7 x^{6})

Entferne die Konstante:

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

= 6 \frac{d}{d x} (6 x^{10} + 7 x^{6})

Wende die Kettenregel an:

\frac{1}{2 6 x ^{10} + 7 x ^{6}} \frac{d}{d x} (6 x^{10} + 7 x^{6})

= \frac{1}{2 6 x ^{10} + 7 x ^{6}} \frac{d}{d x} (6 x^{10} + 7 x^{6})

\frac{d}{d x} (6 x^{10} + 7 x^{6}) = 60 x^{9} + 42 x^{5}

= 6 \cdot \frac{1}{2 6 x ^{10} + 7 x ^{6}} (60 x^{9} + 42 x^{5})

Vereinfache

6 \cdot \frac{1}{2 6 x ^{10} + 7 x ^{6}} (60 x^{9} + 42 x^{5}) : \frac{3 ( 60 x ^{9} + 42 x ^{5} )}{x ^{6} 6 x ^{4} + 7}

= \frac{3 ( 60 x ^{9} + 42 x ^{5} )}{x ^{6} 6 x ^{4} + 7}

s l o p e (0, - 10), (5, - 6)

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