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

Lösung

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

3 x^{2} - 2 x - 5

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= 3 x^{2} - 2 x - 5

d er i v a t i v e f (x) = \frac{5}{x ^{3}}

\int_{0}^{1} 4 x^{2} + 9 x^{4} d x

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

\int 2 e^{9 x} d x

\frac{\partial}{\partial y} (\frac{2 x ^{2} y}{4 + x ^{2} y ^{2}})