derivative of ln(\sqrt[7]{x})

Lösung

\frac{d}{d x} (ln (7 x))

\frac{1}{7 7 x x ^{\frac{6}{7}}}

Schritte zur Lösung

\frac{d}{d x} (ln (7 x))

Wende die Kettenregel an:

\frac{1}{7 x} \frac{d}{d x} (7 x)

= \frac{1}{7 x} \frac{d}{d x} (7 x)

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

= \frac{1}{7 x} \cdot \frac{1}{7 x ^{\frac{6}{7}}}

Vereinfache

\frac{1}{7 x} \cdot \frac{1}{7 x ^{\frac{6}{7}}} : \frac{1}{7 7 x x ^{\frac{6}{7}}}

= \frac{1}{7 7 x x ^{\frac{6}{7}}}

\frac{d}{d x} (2 ∣ x - 3 ∣ - 3 ∣ x - 2 ∣)

\int \frac{( 2 x - 1 )}{( x - 1 ) ( x - 2 )} d x

\frac{e ^{x}}{\frac{d y}{d x}} = (1 + e^{x}) y

y^{^{''}} - 6 y^{^{'}} + 25 y = 50 t^{3} - 36 t^{2} - 63 t + 18

\frac{\partial}{\partial x} (ln (t))