derivative of ln(xsqrt(4x-1))

Lösung

\frac{d}{d x} (ln (x 4 x - 1))

\frac{6 x - 1}{x ( 4 x - 1 )}

Schritte zur Lösung

\frac{d}{d x} (ln (x 4 x - 1))

Wende die Kettenregel an:

\frac{1}{x 4 x - 1} \frac{d}{d x} (x 4 x - 1)

= \frac{1}{x 4 x - 1} \frac{d}{d x} (x 4 x - 1)

\frac{d}{d x} (x 4 x - 1) = \frac{6 x - 1}{4 x - 1}

= \frac{1}{x 4 x - 1} \cdot \frac{6 x - 1}{4 x - 1}

Vereinfache

\frac{1}{x 4 x - 1} \cdot \frac{6 x - 1}{4 x - 1} : \frac{6 x - 1}{x ( 4 x - 1 )}

= \frac{6 x - 1}{x ( 4 x - 1 )}

x \to + 0 lim (\frac{sin ^{2} ( x )}{x})

\int_{3}^{5} e^{x} d x

a re a y = - 2 x, y = 2 x, x = 0, x = 16

t an g e n t f (x) = 8 x^{2} + 3 x

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