derivative of ln(a+x+sqrt(x^2+2ax))

Lösung

\frac{d}{d x} (ln (a + x + x^{2} + 2 a x))

\frac{1}{x ^{2} + 2 a x}

Schritte zur Lösung

\frac{d}{d x} (ln (a + x + x^{2} + 2 a x))

Wende die Kettenregel an:

\frac{1}{a + x + x ^{2} + 2 a x} \frac{d}{d x} (a + x + x^{2} + 2 a x)

= \frac{1}{a + x + x ^{2} + 2 a x} \frac{d}{d x} (a + x + x^{2} + 2 a x)

\frac{d}{d x} (a + x + x^{2} + 2 a x) = \frac{x + a}{x ^{2} + 2 a x} + 1

= \frac{1}{a + x + x ^{2} + 2 a x} (\frac{x + a}{x ^{2} + 2 a x} + 1)

Vereinfache

\frac{1}{a + x + x ^{2} + 2 a x} (\frac{x + a}{x ^{2} + 2 a x} + 1) : \frac{1}{x ^{2} + 2 a x}

= \frac{1}{x ^{2} + 2 a x}

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

\int_{0}^{1} \frac{1}{x ^{1}} d x

\int \frac{x ^{3} + 8}{( x ^{2} - 1 ) ( x - 2 )} d x

\frac{d y}{d x} + (\frac{3}{x} - 1) y = - \frac{2}{x}

a re a y = 2 x, x = 3