derivative x/(x^2+5)

Lösung

ableitung von

\frac{x}{x ^{2} + 5}

\frac{- x ^{2} + 5}{( x ^{2} + 5 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

= \frac{1 \cdot ( x ^{2} + 5 ) - 2 xx}{( x ^{2} + 5 ) ^{2}}

1 \cdot (x^{2} + 5) - 2 xx = - x^{2} + 5

= \frac{- x ^{2} + 5}{( x ^{2} + 5 ) ^{2}}

\int cos^{12} (x) sin^{15} (x) d x

l a pl a ce t r an s f or m cos (15 t)

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

y^{^{''}} + 5 y^{^{'}} + 6 y = 0, y (0) = 2, y^{^{'}} (0) = 0

in v erse l a pl a ce \frac{\frac{1}{s + 1} - 1}{s ^{2} - 1}