derivative of sqrt(6x+6x^2)

Lösung

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

\frac{3 ( 2 x + 1 )}{6 x + 6 x ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (6 x + 6 x^{2}) = 6 + 12 x

= \frac{1}{2 6 x + 6 x ^{2}} (6 + 12 x)

Vereinfache

\frac{1}{2 6 x + 6 x ^{2}} (6 + 12 x) : \frac{3 ( 2 x + 1 )}{6 x + 6 x ^{2}}

= \frac{3 ( 2 x + 1 )}{6 x + 6 x ^{2}}

\frac{d v}{d t} = 0.025 \cdot 7 - \frac{v}{2000}, v (0) = 100

\int_{4}^{10} 0.13 x d x

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\frac{\partial}{\partial y} (x^{2} y + x y^{3})