(\partial)/(\partial x)((x+1)^2(x^2+2x))

Lösung

\frac{\partial}{\partial x} ((x + 1)^{2} (x^{2} + 2 x))

4 x^{3} + 12 x^{2} + 10 x + 2

Schritte zur Lösung

\frac{\partial}{\partial x} ((x + 1)^{2} (x^{2} + 2 x))

Wende die Produktregel an:

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

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

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

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

\frac{\partial}{\partial x} (x^{2} + 2 x) = 2 x + 2

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

Vereinfache

2 (x + 1) (x^{2} + 2 x) + (2 x + 2) (x + 1)^{2} : 4 x^{3} + 12 x^{2} + 10 x + 2

= 4 x^{3} + 12 x^{2} + 10 x + 2

d er i v a t i v e f (x) = \frac{x ^{3} - 1 x ^{2} + 2}{x ^{2}}

\int (x x + 3) d x

\frac{\partial}{\partial x} (x^{4} + y^{4} + 3 x^{2} y^{3})

a re a 13 + 2 x - x^{2}, 3 x + 1

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