derivative f(x)=3sqrt(x)ln(x)

Lösung

ableitung von

f (x) = 3 x ln (x)

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

Schritte zur Lösung

\frac{d}{d x} (3 x ln (x))

Entferne die Konstante:

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

= 3 \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)

= 3 (\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}

= 3 (\frac{1}{2 x} ln (x) + \frac{1}{x} x)

Vereinfache

3 (\frac{1}{2 x} ln (x) + \frac{1}{x} x) : 3 (\frac{ln ( x )}{2 x} + \frac{1}{x})

= 3 (\frac{ln ( x )}{2 x} + \frac{1}{x})

t an g e n t \frac{1}{3} x^{3} - 7 x + 5

n = 1 \sum \infty \frac{x ^{n}}{2 ^{n}}

x \to 0 lim (\frac{f ( x )}{g ( x )})

\int \frac{a + b x ^{3}}{4 a x + b x ^{4}} d x

\frac{d}{d z} (\frac{x y}{z})