(((t^2+1)^{3/2})/3)^'

Lösung

\frac{( t ^{2} + 1 ) ^{\frac{3}{2}}}{3}^{^{'}}

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

Schritte zur Lösung

\frac{( t ^{2} + 1 ) ^{\frac{3}{2}}}{3}^{'}

Entferne die Konstante:

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

= \frac{1}{3} ((t^{2} + 1)^{\frac{3}{2}})^{^{'}}

Wende die Kettenregel an:

\frac{3 ( t ^{2} + 1 ) ^{\frac{1}{2}}}{2} (t^{2} + 1)^{'}

= \frac{3 ( t ^{2} + 1 ) ^{\frac{1}{2}}}{2} (t^{2} + 1)^{'}

(t^{2} + 1)^{'} = 2 t

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

Vereinfache

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

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

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

d er i v a t i v e - 7 (6 x^{2} + 7)^{- 6}

d er i v a t i v e \frac{c ^{4} - x ^{4}}{c ^{4} + x ^{4}}

\int sin (x^{3}) x^{2} d x

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