derivative (x+1)^3(5-x)

Lösung

ableitung von

(x + 1)^{3} (5 - x)

3 (x + 1)^{2} (5 - x) - (x + 1)^{3}

Schritte zur Lösung

\frac{d}{d x} ((x + 1)^{3} (5 - x))

Wende die Produktregel an:

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

f = (x + 1)^{3}, g = 5 - x

= \frac{d}{d x} ((x + 1)^{3}) (5 - x) + \frac{d}{d x} (5 - x) (x + 1)^{3}

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

\frac{d}{d x} (5 - x) = - 1

= 3 (x + 1)^{2} (5 - x) + (- 1) (x + 1)^{3}

Vereinfache

= 3 (x + 1)^{2} (5 - x) - (x + 1)^{3}

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

d er i v a t i v e \frac{( 2 + x )}{( 2 - x )}

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

d er i v a t i v e y = \frac{( x - 3 ) ^{2} - 4}{x ^{2} + 2}

d er i v a t i v e \frac{x ^{2} - 5}{1 - 3 x ^{2}}