derivative f(x)=(x-1)(x+1)^3

Lösung

ableitung von

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

(x + 1)^{3} + 3 (x + 1)^{2} (x - 1)

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x - 1, g = (x + 1)^{3}

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

\frac{d}{d x} (x - 1) = 1

\frac{d}{d x} ((x + 1)^{3}) = 3 (x + 1)^{2}

= 1 \cdot (x + 1)^{3} + 3 (x + 1)^{2} (x - 1)

Vereinfache

= (x + 1)^{3} + 3 (x + 1)^{2} (x - 1)

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

d er i v a t i v e - \frac{9}{( 6 t + 8 ) ^{\frac{3}{2}}}

x \to 1 - lim (\frac{4}{x ^{3} - 1})

\frac{d}{d x} (3 (x)^{3} + cos (x))

x \to 0 lim (x^{2} csc^{2} (x))