derivative (3t^5-1)/(x^2+2)

Lösung

ableitung von

\frac{3 t ^{5} - 1}{x ^{2} + 2}

\frac{15 t ^{4}}{x ^{2} + 2}

Schritte zur Lösung

\frac{d}{d t} (\frac{3 t ^{5} - 1}{x ^{2} + 2})

Behandle

x

als Konstante

Entferne die Konstante:

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

= \frac{1}{x ^{2} + 2} \frac{d}{d t} (3 t^{5} - 1)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{x ^{2} + 2} (\frac{d}{d t} (3 t^{5}) - \frac{d}{d t} (1))

\frac{d}{d t} (3 t^{5}) = 15 t^{4}

\frac{d}{d t} (1) = 0

= \frac{1}{x ^{2} + 2} (15 t^{4} - 0)

Vereinfache

\frac{1}{x ^{2} + 2} (15 t^{4} - 0) : \frac{15 t ^{4}}{x ^{2} + 2}

= \frac{15 t ^{4}}{x ^{2} + 2}

\int 10 t^{2} + 7 t - 9 d t

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

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

x \to - \infty lim (\frac{( 5 x ^{2} - 2 )}{x + 3})

x \to 0 lim (\frac{∣ x - 1 ∣ - 1}{x})