derivative of (x-1^2(2x+3))

Lösung

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

6 x^{2} - 2 x - 4

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 (x - 1) (2 x + 3) + 2 (x - 1)^{2} : 6 x^{2} - 2 x - 4

= 6 x^{2} - 2 x - 4

\int_{- 3}^{- 1} \frac{1}{x ^{2} + 6 x + 13} d x

\int \frac{1}{( x + 3 ) x ^{2} + 6 x + 8} d x

\int (5 x^{4}) d x

7 (ln (y)) y^{^{'}} - x^{9} y = 0

d er i v a t i v e (f (4 x))^{2} + 5