derivative f(x)=(x+1)^2(x-4)^3

Lösung

ableitung von

f (x) = (x + 1)^{2} (x - 4)^{3}

2 (x + 1) (x - 4)^{3} + 3 (x - 4)^{2} (x + 1)^{2}

Schritte zur Lösung

\frac{d}{d x} ((x + 1)^{2} (x - 4)^{3})

Wende die Produktregel an:

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

f = (x + 1)^{2}, g = (x - 4)^{3}

= \frac{d}{d x} ((x + 1)^{2}) (x - 4)^{3} + \frac{d}{d x} ((x - 4)^{3}) (x + 1)^{2}

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

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

= 2 (x + 1) (x - 4)^{3} + 3 (x - 4)^{2} (x + 1)^{2}

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

d er i v a t i v e y = (x^{2} + 3)^{2}

d er i v a t i v e y = arctan (x - 1 + x^{2})

d er i v a t i v e f (x) = x^{3} e^{x}

t an g e n t f (x) = 3 x^{2}, at x = 2