derivative 3x*ln(1/(x^2))

Lösung

ableitung von

3 x \cdot ln (\frac{1}{x ^{2}})

- 3 (ln (x^{2}) + 2)

Schritte zur Lösung

\frac{d}{d x} (3 x ln (\frac{1}{x ^{2}}))

Vereinfache

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

= \frac{d}{d x} (- 3 x ln (x^{2}))

Entferne die Konstante:

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

= - 3 \frac{d}{d x} (x ln (x^{2}))

Wende die Produktregel an:

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

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

= - 3 (ln (x^{2}) + 2)

\int_{4}^{\infty} x e^{- 5 x} d x

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

x \to - 1 lim (\frac{4 x ^{2} + 1}{x})

\int - x \cdot e^{- x} d x

\int \frac{e ^{2 x} + 2 e ^{x}}{e ^{2 x} - 8} d x