derivative (6x^2+8x+8x)/(sqrt(x))

Lösung

ableitung von

\frac{6 x ^{2} + 8 x + 8 x}{x}

\frac{9 x + 8}{x}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 x ^{2} + 8 x + 8 x}{x})

Vereinfache

\frac{6 x ^{2} + 8 x + 8 x}{x} : 2 x (3 x + 8)

= \frac{d}{d x} (2 x (3 x + 8))

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x (3 x + 8))

Wende die Produktregel an:

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

f = x, g = 3 x + 8

= 2 (\frac{d}{d x} (x) (3 x + 8) + \frac{d}{d x} (3 x + 8) x)

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (3 x + 8) = 3

= 2 (\frac{1}{2 x} (3 x + 8) + 3 x)

Vereinfache

2 (\frac{1}{2 x} (3 x + 8) + 3 x) : \frac{9 x + 8}{x}

= \frac{9 x + 8}{x}

y^{^{'}} = \frac{( y ^{2} + 2 x y )}{x ^{2}}

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