derivative (75x)/(x^2+100)

Lösung

ableitung von

\frac{75 x}{x ^{2} + 100}

\frac{75 ( - x ^{2} + 100 )}{( x ^{2} + 100 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{75 x}{x ^{2} + 100})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 75 \frac{d}{d x} (\frac{x}{x ^{2} + 100})

Wende die Quotientenregel an:

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

= 75 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 100 ) - \frac{d}{d x} ( x ^{2} + 100 ) x}{( x ^{2} + 100 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 100) = 2 x

= 75 \cdot \frac{1 \cdot ( x ^{2} + 100 ) - 2 xx}{( x ^{2} + 100 ) ^{2}}

Vereinfache

75 \cdot \frac{1 \cdot ( x ^{2} + 100 ) - 2 xx}{( x ^{2} + 100 ) ^{2}} : \frac{75 ( - x ^{2} + 100 )}{( x ^{2} + 100 ) ^{2}}

= \frac{75 ( - x ^{2} + 100 )}{( x ^{2} + 100 ) ^{2}}

d er i v a t i v e 1 - 2 x

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

y^{^{''}} - 9 y = 0, y (0) = 6

x \to 54 lim (\frac{x ^{2}}{6} - \frac{9}{x})

x \to 2 lim (5 x^{2} - 2 x + 3)