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

Lösung

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

3 x^{2} + 1

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

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

= 3 x^{2} + 1

in v erse l a pl a ce \frac{3}{s - 5} - \frac{2}{s + 7}

\int b^{x} d x

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

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

l a pl a ce t r an s f or m 2 t cos (t)