derivative of ln(axsqrt(a+x))

Lösung

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

\frac{3 x + 2 a}{2 x ( a + x )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (a x a + x) = \frac{a ( 3 x + 2 a )}{2 a + x}

= \frac{1}{a x a + x} \cdot \frac{a ( 3 x + 2 a )}{2 a + x}

Vereinfache

\frac{1}{a x a + x} \cdot \frac{a ( 3 x + 2 a )}{2 a + x} : \frac{3 x + 2 a}{2 x ( a + x )}

= \frac{3 x + 2 a}{2 x ( a + x )}

\int \frac{1}{( x ^{2} - 49 ) ^{\frac{3}{2}}} d x

- y^{^{'}} + \frac{2 y}{x} = x^{3} y^{2}

t \to 0 lim (\frac{6}{1 + t})

d er i v a t i v e f (x) = arcsin (x)

\int 1 + (2 x)^{2} d x