derivative of (3x^2+5x/(sqrt(x)))

Lösung

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

\frac{9 x + 5}{2 x}

Schritte zur Lösung

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

Vereinfache

\frac{3 x ^{2} + 5 x}{x} : x (3 x + 5)

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

Wende die Produktregel an:

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

f = x, g = 3 x + 5

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

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

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

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

Vereinfache

\frac{1}{2 x} (3 x + 5) + 3 x : \frac{9 x + 5}{2 x}

= \frac{9 x + 5}{2 x}

\frac{d ^{10}}{d x ^{10}} (cos (2 x))

t^{2} \cdot \frac{d x}{d t} = \frac{1}{x}

\frac{d}{d x} (8 x e^{4 x})

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