derivative of 1/6 \sqrt[5]{(6-5x^2^7})

Lösung

\frac{d}{d x} (\frac{1}{6} 5 (6 - 5 x^{2})^{7})

- \frac{7 x ( - 5 x ^{2} + 6 ) ^{\frac{2}{5}}}{3}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{6} 5 (6 - 5 x^{2})^{7})

Entferne die Konstante:

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

= \frac{1}{6} \frac{d}{d x} (5 (6 - 5 x^{2})^{7})

Wende die Kettenregel an:

\frac{1}{5 ( ( 6 - 5 x ^{2} ) ^{7} ) ^{\frac{4}{5}}} \frac{d}{d x} ((6 - 5 x^{2})^{7})

= \frac{1}{5 ( ( 6 - 5 x ^{2} ) ^{7} ) ^{\frac{4}{5}}} \frac{d}{d x} ((6 - 5 x^{2})^{7})

\frac{d}{d x} ((6 - 5 x^{2})^{7}) = - 70 x (6 - 5 x^{2})^{6}

= \frac{1}{6} \cdot \frac{1}{5 ( ( 6 - 5 x ^{2} ) ^{7} ) ^{\frac{4}{5}}} (- 70 x (6 - 5 x^{2})^{6})

Vereinfache

\frac{1}{6} \cdot \frac{1}{5 ( ( 6 - 5 x ^{2} ) ^{7} ) ^{\frac{4}{5}}} (- 70 x (6 - 5 x^{2})^{6}) : - \frac{7 x ( - 5 x ^{2} + 6 ) ^{\frac{2}{5}}}{3}

= - \frac{7 x ( - 5 x ^{2} + 6 ) ^{\frac{2}{5}}}{3}

\int \frac{x}{3 x - 1} d x

\int x e^{- \frac{1}{10} x^{2}} d x

\frac{d ^{3}}{d x ^{3}} ((1 + x)^{3})

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

y^{^{'}} - (\frac{3}{t}) \cdot y = 2 t^{3} \cdot e^{(2 t)}, y (1) = 0