derivative x/(x^2+25)

Lösung

ableitung von

\frac{x}{x ^{2} + 25}

\frac{- x ^{2} + 25}{( x ^{2} + 25 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{2} + 25})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 25 ) - \frac{d}{d x} ( x ^{2} + 25 ) x}{( x ^{2} + 25 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 25) = 2 x

= \frac{1 \cdot ( x ^{2} + 25 ) - 2 xx}{( x ^{2} + 25 ) ^{2}}

1 \cdot (x^{2} + 25) - 2 xx = - x^{2} + 25

= \frac{- x ^{2} + 25}{( x ^{2} + 25 ) ^{2}}

\int \frac{- 2 ln ( x )}{x} d x

\int x^{2} 0. 4^{- x} d x

\int \frac{y ^{2}}{( 4 - y ^{2} ) ^{\frac{3}{2}}} d y

t an g e n t f (x) = - 18 x - \frac{17}{x}

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