derivative \sqrt[3]{(x^2-1)^2}

Lösung

ableitung von

3 (x^{2} - 1)^{2}

\frac{4 x ( x ^{2} - 1 )}{3 ( ( x ^{2} - 1 ) ^{2} ) ^{\frac{2}{3}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} ((x^{2} - 1)^{2}) = 4 x (x^{2} - 1)

= \frac{1}{3 ( ( x ^{2} - 1 ) ^{2} ) ^{\frac{2}{3}}} \cdot 4 x (x^{2} - 1)

Vereinfache

\frac{1}{3 ( ( x ^{2} - 1 ) ^{2} ) ^{\frac{2}{3}}} \cdot 4 x (x^{2} - 1) : \frac{4 x ( x ^{2} - 1 )}{3 ( ( x ^{2} - 1 ) ^{2} ) ^{\frac{2}{3}}}

= \frac{4 x ( x ^{2} - 1 )}{3 ( ( x ^{2} - 1 ) ^{2} ) ^{\frac{2}{3}}}

\frac{d y}{d x} = \frac{3 x}{5 y}

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

\int 2 4 x d x

\int \frac{tan ( ln ( y ) )}{y} d y

\int 120 x (2 x + 120)^{4} d x