derivative of sqrt((x^2-1/(x^2+1)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{2 \frac{x ^{2} - 1}{x ^{2} + 1}} \cdot \frac{4 x}{( x ^{2} + 1 ) ^{2}}

Vereinfache

\frac{1}{2 \frac{x ^{2} - 1}{x ^{2} + 1}} \cdot \frac{4 x}{( x ^{2} + 1 ) ^{2}} : \frac{2 x}{x ^{2} - 1 ( x ^{2} + 1 ) ^{\frac{3}{2}}}

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

\frac{d}{d x} ((6 x + 5)^{x})

n = 0 \sum \infty \frac{x ^{n}}{2 n !}

t a y l or e^{(- \frac{x}{2})}, 0

\frac{d}{d x} (e^{x} sin (5 x))

\frac{d}{d x} (100 x^{\frac{3}{4}} y^{\frac{1}{4}})