derivative of-9(3x^4-x^3+2x^5)

Lösung

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

- 45 (3 x^{4} - x^{3} + 2 x)^{4} (12 x^{3} - 3 x^{2} + 2)

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (3 x^{4} - x^{3} + 2 x) = 12 x^{3} - 3 x^{2} + 2

= - 9 \cdot 5 (3 x^{4} - x^{3} + 2 x)^{4} (12 x^{3} - 3 x^{2} + 2)

Vereinfache

= - 45 (3 x^{4} - x^{3} + 2 x)^{4} (12 x^{3} - 3 x^{2} + 2)

\frac{\partial}{\partial y} (2 x - 3 y + 5)

d er i v a t i v e (x^{2} + 2) (x^{3} + 6)

\int cos (x) e^{- s x} d x

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

s l o p e (\frac{5}{8}, - 2), (- \frac{1}{4}, - \frac{1}{4})