derivative of x^2ln(x/2)

Lösung

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

2 x ln (\frac{x}{2}) + x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

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

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

x \to \frac{2}{3} lim (\frac{3 x - 2}{3 x ^{2} - 11 x + 6})

\frac{\partial}{\partial z} (x y + yz + z x)

\frac{d}{d x} (x cos^{3} (x))

\int_{1}^{2} x ln (x) d x

\frac{d}{d x} (e^{(- 3 x)})