(\partial)/(\partial x)(2/3 (x^2+1)^{3/2})

Lösung

\frac{\partial}{\partial x} (\frac{2}{3} (x^{2} + 1)^{\frac{3}{2}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{2}{3} (x^{2} + 1)^{\frac{3}{2}})

Entferne die Konstante:

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

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

Wende die Kettenregel an:

\frac{3 ( x ^{2} + 1 ) ^{\frac{1}{2}}}{2} \frac{\partial}{\partial x} (x^{2} + 1)

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

\frac{\partial}{\partial x} (x^{2} + 1) = 2 x

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

Vereinfache

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

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

y^{^{''}} - 0.02 y = 0, y^{^{'}} (0) = 2, y (0) = 0

x \to 2 lim (x^{3} f (2))

\int \frac{2}{x x ^{2} - 9} d x

d er i v a t i v e y = 3 x^{- 2} - 5 x^{- 3} + 3 x^{- 1}

\frac{\partial}{\partial y} (x tan (y + z))