derivative 9arctan(x-sqrt(1+x^2))

Lösung

ableitung von

9 arctan (x - 1 + x^{2})

\frac{9 ( 1 + x ^{2} - x )}{( 2 x ^{2} - 2 x x ^{2} + 1 + 2 ) 1 + x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (9 arctan (x - 1 + x^{2}))

Entferne die Konstante:

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

= 9 \frac{d}{d x} (arctan (x - 1 + x^{2}))

Wende die Kettenregel an:

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

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

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

= 9 \cdot \frac{1}{( x - 1 + x ^{2} ) ^{2} + 1} (1 - \frac{x}{1 + x ^{2}})

Vereinfache

9 \cdot \frac{1}{( x - 1 + x ^{2} ) ^{2} + 1} (1 - \frac{x}{1 + x ^{2}}) : \frac{9 ( 1 + x ^{2} - x )}{( 2 x ^{2} - 2 x x ^{2} + 1 + 2 ) 1 + x ^{2}}

= \frac{9 ( 1 + x ^{2} - x )}{( 2 x ^{2} - 2 x x ^{2} + 1 + 2 ) 1 + x ^{2}}

s l o p e (19, - 16), (- 7, - 15)

x \to 2 lim (x^{3})

d er i v a t i v e 7 x e^{x}

\frac{\partial}{\partial y} (- \frac{y}{( x + 2 ) ^{2}})

\frac{d}{d x} (\frac{x ^{2} + 1}{3 x ^{3} + 4 x})