derivative f(x)=2x^2ln(2x)

Lösung

ableitung von

f (x) = 2 x^{2} ln (2 x)

2 (2 x ln (2 x) + x)

Schritte zur Lösung

\frac{d}{d x} (2 x^{2} ln (2 x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (x^{2} ln (2 x))

Wende die Produktregel an:

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

f = x^{2}, g = ln (2 x)

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

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

\frac{d}{d x} (ln (2 x)) = \frac{1}{x}

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

\frac{1}{x} x^{2} = x

= 2 (2 x ln (2 x) + x)

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

\int (x - 2 y) d y

t an g e n t \frac{18}{x}

\int t^{- 4} d t

\frac{d}{d x} (\frac{x ^{2} + x - 2}{x ^{3} + 6})