derivative y=ln(x^2sqrt(x+1))

Lösung

ableitung von

y = ln (x^{2} x + 1)

\frac{5 x + 4}{2 x ( x + 1 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x^{2} x + 1) = \frac{5 x ^{2} + 4 x}{2 x + 1}

= \frac{1}{x ^{2} x + 1} \cdot \frac{5 x ^{2} + 4 x}{2 x + 1}

Vereinfache

\frac{1}{x ^{2} x + 1} \cdot \frac{5 x ^{2} + 4 x}{2 x + 1} : \frac{5 x + 4}{2 x ( x + 1 )}

= \frac{5 x + 4}{2 x ( x + 1 )}

x \to 8 - lim (\frac{1}{x - 8})

x \to 2 + lim (\frac{x}{4 - x ^{2}})

\int \frac{x}{x ^{4} + 2 x ^{2} + 2} d x

x \to 2 π - lim ((x) csc (x))

in v erse l a pl a ce {\frac{( s + 1 ) ^{3}}{s ^{4}}}