derivative 4sqrt(x)ln(x)

Lösung

ableitung von

4 x ln (x)

4 (\frac{ln ( x )}{2 x} + \frac{1}{x})

Schritte zur Lösung

\frac{d}{d x} (4 x ln (x))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x ln (x))

Wende die Produktregel an:

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

f = x, g = ln (x)

= 4 (\frac{d}{d x} (x) ln (x) + \frac{d}{d x} (ln (x)) x)

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

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

= 4 (\frac{1}{2 x} ln (x) + \frac{1}{x} x)

Vereinfache

4 (\frac{1}{2 x} ln (x) + \frac{1}{x} x) : 4 (\frac{ln ( x )}{2 x} + \frac{1}{x})

= 4 (\frac{ln ( x )}{2 x} + \frac{1}{x})

\frac{\partial}{\partial y} (5 x^{2} - 3 x y^{2} + x yz)

n \to \infty lim (2 n)

x \to \infty lim (\frac{2 x ^{2}}{- x + 2})

ma c l a u r in \frac{x}{1 + 4 x ^{2}}, 6

\frac{\partial}{\partial x} (in x y)