derivative sqrt(t+t^3)

Lösung

ableitung von

t + t^{3}

\frac{1 + 3 t ^{2}}{2 t + t ^{3}}

Schritte zur Lösung

\frac{d}{d t} (t + t^{3})

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{1 + 3 t ^{2}}{2 t + t ^{3}}

\frac{d y}{d x} = 8 - 4 y

\int \frac{e ^{2 x}}{3 x} d x

\frac{d}{d x} (x^{3} - 4 x + 7)

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

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