d/(dt)(ln(a+{v}(t)t))

Lösung

\frac{d}{d t} (ln (a + v (t) t))

\frac{t \frac{d}{d t} ( v ( t ) ) + v ( t )}{a + t v ( t )}

Schritte zur Lösung

\frac{d}{d t} (ln (a + v (t) t))

Wende die Kettenregel an:

\frac{1}{a + v ( t ) t} \frac{d}{d t} (a + v (t) t)

= \frac{1}{a + v ( t ) t} \frac{d}{d t} (a + v (t) t)

\frac{d}{d t} (a + v (t) t) = t \frac{d}{d t} (v (t)) + v (t)

= \frac{1}{a + v ( t ) t} (t \frac{d}{d t} (v (t)) + v (t))

Vereinfache

\frac{1}{a + v ( t ) t} (t \frac{d}{d t} (v (t)) + v (t)) : \frac{t \frac{d}{d t} ( v ( t ) ) + v ( t )}{a + t v ( t )}

= \frac{t \frac{d}{d t} ( v ( t ) ) + v ( t )}{a + t v ( t )}

\frac{d}{d x} ((- 1)^{n} x^{2 n})

y^{^{'}} = 0.5 y, y (2) = 100

x \to - 1 lim (\frac{∣ x + 1 ∣}{x + 1})

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

\int \frac{x ^{2} + 1}{x ^{3} + 3 x - 16} d x