derivative of (4(-x^2+4)/((x^2+4)^2))

Lösung

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

- \frac{8 x ( - x ^{2} + 12 )}{( x ^{2} + 4 ) ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

4 \cdot \frac{( - 2 x ) ( x ^{2} + 4 ) ^{2} - 4 x ( x ^{2} + 4 ) ( - x ^{2} + 4 )}{( ( x ^{2} + 4 ) ^{2} ) ^{2}} : - \frac{8 x ( - x ^{2} + 12 )}{( x ^{2} + 4 ) ^{3}}

= - \frac{8 x ( - x ^{2} + 12 )}{( x ^{2} + 4 ) ^{3}}

x \to 3 lim ((8) + 6 (- 7))

f (x) = (arctan (9 x))^{2}

\int x^{0.5} d x

d er i v a t i v e f (x) = 4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 2 x

t an g e n t f (x) = \frac{2}{x}, at \frac{1}{16}