derivative of 2+3/(1+(x+1^2))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (2) = 0

\frac{d}{d x} (\frac{3}{x ^{2} + 2 x + 2}) = - \frac{3 ( 2 x + 2 )}{( x ^{2} + 2 x + 2 ) ^{2}}

= 0 - \frac{3 ( 2 x + 2 )}{( x ^{2} + 2 x + 2 ) ^{2}}

Vereinfache

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

\frac{d}{d x} (8 x sin (x))

x \to - 3 + lim (\frac{x - 3}{x - 4})

\frac{d}{d x} (\frac{e ^{x^{2}}}{( 2 x + 1 ) ^{5}})

\frac{\partial}{\partial y} (4 x y^{3})

n = 1 \sum \infty \frac{2}{n \cdot ( n + 2 )}