derivative of 3000(1+(4x/(x^2+100)))

Lösung

\frac{d}{d x} (3000 (1 + \frac{4 x}{x ^{2} + 100}))

\frac{12000 ( - x ^{2} + 100 )}{( x ^{2} + 100 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (3000 (1 + \frac{4 x}{x ^{2} + 100}))

Entferne die Konstante:

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

= 3000 \frac{d}{d x} (1 + \frac{4 x}{x ^{2} + 100})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 3000 (\frac{d}{d x} (1) + \frac{d}{d x} (\frac{4 x}{x ^{2} + 100}))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (\frac{4 x}{x ^{2} + 100}) = \frac{4 ( - x ^{2} + 100 )}{( x ^{2} + 100 ) ^{2}}

= 3000 (0 + \frac{4 ( - x ^{2} + 100 )}{( x ^{2} + 100 ) ^{2}})

Vereinfache

3000 (0 + \frac{4 ( - x ^{2} + 100 )}{( x ^{2} + 100 ) ^{2}}) : \frac{12000 ( - x ^{2} + 100 )}{( x ^{2} + 100 ) ^{2}}

= \frac{12000 ( - x ^{2} + 100 )}{( x ^{2} + 100 ) ^{2}}

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

2 y^{^{''}} + 3 y^{^{'}} + 4 y = 0

\int x - x^{4} d x

\frac{d}{d x} (\frac{5 x - 2}{2 x + 7})

y^{^{''}} - 3 y^{^{'}} - 28 y = 0