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

Lösung

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

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

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

\frac{\partial}{\partial x} (- cos^{2} (x))

\int \frac{x}{x ^{2} + 36} d x

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

t a y l or x^{2} e^{3 x}

y^{^{''}} - 6 y^{^{'}} - 7 y = 0, y (0) = b, y^{^{'}} (0) = 8