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

Lösung

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

4 x^{3} - 4 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{2} - a - 1, g = x^{2} + a - 1

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

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

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

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

Vereinfache

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

= 4 x^{3} - 4 x

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

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

y = (1 + 4 (2))^{\frac{3}{2}}

\int_{0}^{x} 36 - t^{2} d t

\frac{d}{d x} ((2 x^{5} - 3)^{8})