derivative f(x)=((2x+1)/(x+5))(3x-1)

Lösung

ableitung von

f (x) = (\frac{2 x + 1}{x + 5}) (3 x - 1)

\frac{6 x ^{2} + 60 x + 6}{( x + 5 ) ^{2}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = \frac{2 x + 1}{x + 5}, g = 3 x - 1

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

\frac{d}{d x} (\frac{2 x + 1}{x + 5}) = \frac{9}{( x + 5 ) ^{2}}

\frac{d}{d x} (3 x - 1) = 3

= \frac{9}{( x + 5 ) ^{2}} (3 x - 1) + 3 \cdot \frac{2 x + 1}{x + 5}

Vereinfache

\frac{9}{( x + 5 ) ^{2}} (3 x - 1) + 3 \cdot \frac{2 x + 1}{x + 5} : \frac{6 x ^{2} + 60 x + 6}{( x + 5 ) ^{2}}

= \frac{6 x ^{2} + 60 x + 6}{( x + 5 ) ^{2}}

\frac{d ^{2}}{d x ^{2}} (\frac{6}{7 t ^{4}})

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