derivative 4x^3-33x^2+84x-60

Lösung

ableitung von

4 x^{3} - 33 x^{2} + 84 x - 60

12 x^{2} - 66 x + 84

Schritte zur Lösung

\frac{d}{d x} (4 x^{3} - 33 x^{2} + 84 x - 60)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x^{3}) - \frac{d}{d x} (33 x^{2}) + \frac{d}{d x} (84 x) - \frac{d}{d x} (60)

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

\frac{d}{d x} (33 x^{2}) = 66 x

\frac{d}{d x} (84 x) = 84

\frac{d}{d x} (60) = 0

= 12 x^{2} - 66 x + 84 - 0

Vereinfache

= 12 x^{2} - 66 x + 84

\frac{d}{d x} (2 x 16 - x^{2})

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

d er i v a t i v e f (x) = \frac{2 x ^{\frac{3}{2}} - x ^{2} + 4}{x}

d er i v a t i v e \frac{500}{12 + 5 e ^{- 0.5 t}}

im pl i c i t \frac{d y}{d x}, x = y^{3} - 8 y^{2} + 5, (- 2, 1)