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

Lösung

ableitung von

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{\partial}{\partial x} (\frac{x}{a})

\int - \frac{25}{x ^{26}} d x

t^{2} \cdot y^{^{'}} + t \cdot y = 7

\int x^{3} cos (x^{4}) d x

\frac{\partial}{\partial x} (cos (e^{- x^{2}}))