derivative of (-3x^6-x^5+3x^4/(x^2))

Lösung

\frac{d}{d x} (\frac{- 3 x ^{6} - x ^{5} + 3 x ^{4}}{x ^{2}})

- 12 x^{3} - 3 x^{2} + 6 x

Schritte zur Lösung

\frac{d}{d x} (\frac{- 3 x ^{6} - x ^{5} + 3 x ^{4}}{x ^{2}})

Vereinfache

\frac{- 3 x ^{6} - x ^{5} + 3 x ^{4}}{x ^{2}} : x^{2} (- 3 x^{2} - x + 3)

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

Wende die Produktregel an:

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

f = x^{2}, g = - 3 x^{2} - x + 3

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

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

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

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

Vereinfache

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

= - 12 x^{3} - 3 x^{2} + 6 x

x y^{^{'}} + y = y^{2}

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

\int \frac{x}{- x ^{2} + 4} d x

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