derivative of x(x-1^4)

Lösung

\frac{d}{d x} (x (x - 1)^{4})

(x - 1)^{4} + 4 x (x - 1)^{3}

Schritte zur Lösung

\frac{d}{d x} (x (x - 1)^{4})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (x - 1)^{4}

= \frac{d x}{d x} (x - 1)^{4} + \frac{d}{d x} ((x - 1)^{4}) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((x - 1)^{4}) = 4 (x - 1)^{3}

= 1 \cdot (x - 1)^{4} + 4 (x - 1)^{3} x

Vereinfache

= (x - 1)^{4} + 4 x (x - 1)^{3}

\frac{\partial}{\partial x} (x y + yz + x z)

y^{^{''}} - 4 y^{^{'}} + 4 y = 2 + 8 x - 4 x^{2}

s l o p e in t erce pt (- 1, - 2), (0, 5)

\frac{d}{d x} (\frac{1 - 4 e ^{x}}{1 - 5 cos ( x )})

d er i v a t i v e f (x) = \frac{1}{2} arctan (\frac{x}{2})