derivative of x^4-8x^3+22x^2-24x+9

Lösung

\frac{d}{d x} (x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 9)

4 x^{3} - 24 x^{2} + 44 x - 24

Schritte zur Lösung

\frac{d}{d x} (x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 9)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (8 x^{3}) + \frac{d}{d x} (22 x^{2}) - \frac{d}{d x} (24 x) + \frac{d}{d x} (9)

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

\frac{d}{d x} (8 x^{3}) = 24 x^{2}

\frac{d}{d x} (22 x^{2}) = 44 x

\frac{d}{d x} (24 x) = 24

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

= 4 x^{3} - 24 x^{2} + 44 x - 24 + 0

Vereinfache

= 4 x^{3} - 24 x^{2} + 44 x - 24

t an g e n t x^{4} + x y^{2} = 5, (1, 2)

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

\frac{\partial}{\partial x} (\frac{x}{x + y} + e^{x y} x + 4 y)

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

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