derivative 3x^3-5x+7x^4-9-x^2

Lösung

ableitung von

3 x^{3} - 5 x + 7 x^{4} - 9 - x^{2}

28 x^{3} + 9 x^{2} - 2 x - 5

Schritte zur Lösung

\frac{d}{d x} (3 x^{3} - 5 x + 7 x^{4} - 9 - x^{2})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (3 x^{3}) - \frac{d}{d x} (5 x) + \frac{d}{d x} (7 x^{4}) - \frac{d}{d x} (9) - \frac{d}{d x} (x^{2})

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

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

\frac{d}{d x} (7 x^{4}) = 28 x^{3}

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

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

= 9 x^{2} - 5 + 28 x^{3} - 0 - 2 x

Vereinfache

= 28 x^{3} + 9 x^{2} - 2 x - 5