derivative of x^{9/5}y^7z^{2/7}

Lösung

\frac{d}{d x} (x^{\frac{9}{5}} y^{7} z^{\frac{2}{7}})

\frac{9 y ^{7} z ^{\frac{2}{7}} x ^{\frac{4}{5}}}{5}

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{9}{5}} y^{7} z^{\frac{2}{7}})

Entferne die Konstante:

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

= y^{7} z^{\frac{2}{7}} \frac{d}{d x} (x^{\frac{9}{5}})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= y^{7} z^{\frac{2}{7}} \frac{9}{5} x^{\frac{9}{5} - 1}

Vereinfache

y^{7} z^{\frac{2}{7}} \frac{9}{5} x^{\frac{9}{5} - 1} : \frac{9 y ^{7} z ^{\frac{2}{7}} x ^{\frac{4}{5}}}{5}

= \frac{9 y ^{7} z ^{\frac{2}{7}} x ^{\frac{4}{5}}}{5}

y^{^{'}} = \frac{1}{10} y (500 - y)

t a y l or x^{5}, x = 2

t an g e n t y = x^{2} + 3 x + 11

t a y l or \frac{3}{1 + 3 x}

\int x 5 + 2 x d x