d/(dt)(t^{-2}ln(t))

Lösung

\frac{d}{d t} (t^{- 2} ln (t))

\frac{- 2 ln ( t ) + 1}{t ^{3}}

Schritte zur Lösung

\frac{d}{d t} (t^{- 2} ln (t))

Wende die Produktregel an:

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

f = t^{- 2}, g = ln (t)

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (1 - x^{2})

\frac{\partial}{\partial y} (x^{4} sin (x y^{3}))

x \to \infty lim (\frac{lo g _{2} ( x )}{x})

f (x) = 2 x^{4}

\int \frac{x ^{2} - 1}{x ^{2}} d x