derivative of ln(x^3+7/(sqrt(x)))

Lösung

\frac{d}{d x} (ln (x^{3}) + \frac{7}{x})

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

Schritte zur Lösung

\frac{d}{d x} (ln (x^{3}) + \frac{7}{x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (ln (x^{3})) + \frac{d}{d x} (\frac{7}{x})

\frac{d}{d x} (ln (x^{3})) = \frac{3}{x}

\frac{d}{d x} (\frac{7}{x}) = - \frac{7}{2 x ^{\frac{3}{2}}}

= \frac{3}{x} - \frac{7}{2 x ^{\frac{3}{2}}}

Vereinfache

\frac{3}{x} - \frac{7}{2 x ^{\frac{3}{2}}} : \frac{6 x ^{\frac{3}{2}} - 7 x}{2 x ^{\frac{5}{2}}}

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

\int \frac{5}{x ^{2} + 6 x + 10} d x

\frac{d}{d x} (\frac{x - 4}{x ^{2} - 2 x + 8})

\frac{\partial}{\partial x} ((x^{2} - y^{2}) ln (x y))

\frac{d}{d x} (9 sin^{2} (x))

a re a y = x^{2} - 14, y = 13 x