derivative p(x)=2x^4+3x^3-6x^2+9

Lösung

ableitung von

p (x) = 2 x^{4} + 3 x^{3} - 6 x^{2} + 9

8 x^{3} + 9 x^{2} - 12 x

Schritte zur Lösung

\frac{d}{d x} (2 x^{4} + 3 x^{3} - 6 x^{2} + 9)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x^{4}) + \frac{d}{d x} (3 x^{3}) - \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (9)

\frac{d}{d x} (2 x^{4}) = 8 x^{3}

\frac{d}{d x} (3 x^{3}) = 9 x^{2}

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

\frac{d}{d x} (9) = 0

= 8 x^{3} + 9 x^{2} - 12 x + 0

Vereinfache

= 8 x^{3} + 9 x^{2} - 12 x

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\frac{d}{d x} (9 sin (x))

\frac{d}{d x} (2 x^{- 1})

\int_{4}^{6} \frac{y}{y ^{2} - 3} d y