derivative 5x^4-28x^3+42x^2-196x+49

Lösung

ableitung von

5 x^{4} - 28 x^{3} + 42 x^{2} - 196 x + 49

20 x^{3} - 84 x^{2} + 84 x - 196

Schritte zur Lösung

\frac{d}{d x} (5 x^{4} - 28 x^{3} + 42 x^{2} - 196 x + 49)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (5 x^{4}) - \frac{d}{d x} (28 x^{3}) + \frac{d}{d x} (42 x^{2}) - \frac{d}{d x} (196 x) + \frac{d}{d x} (49)

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

\frac{d}{d x} (28 x^{3}) = 84 x^{2}

\frac{d}{d x} (42 x^{2}) = 84 x

\frac{d}{d x} (196 x) = 196

\frac{d}{d x} (49) = 0

= 20 x^{3} - 84 x^{2} + 84 x - 196 + 0

Vereinfache

= 20 x^{3} - 84 x^{2} + 84 x - 196

x \to 0 lim (tan^{4} (4 x))

n or ma l y = 5 x^{3} - 3 x, (1, 2)

x \to a lim (3 x^{2} - 2)

x \to \infty lim (24 x^{7} e^{- x^{8}}, [0, x])

\frac{\partial}{\partial y} (x e^{3 x y})