derivative (x+1)/(4x^2+12x+2)

Lösung

ableitung von

\frac{x + 1}{4 x ^{2} + 12 x + 2}

- \frac{2 x ^{2} + 4 x + 5}{2 ( 2 x ^{2} + 6 x + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 1}{4 x ^{2} + 12 x + 2})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x + 1 ) ( 4 x ^{2} + 12 x + 2 ) - \frac{d}{d x} ( 4 x ^{2} + 12 x + 2 ) ( x + 1 )}{( 4 x ^{2} + 12 x + 2 ) ^{2}}

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

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

= \frac{1 \cdot ( 4 x ^{2} + 12 x + 2 ) - ( 8 x + 12 ) ( x + 1 )}{( 4 x ^{2} + 12 x + 2 ) ^{2}}

Vereinfache

\frac{1 \cdot ( 4 x ^{2} + 12 x + 2 ) - ( 8 x + 12 ) ( x + 1 )}{( 4 x ^{2} + 12 x + 2 ) ^{2}} : - \frac{2 x ^{2} + 4 x + 5}{2 ( 2 x ^{2} + 6 x + 1 ) ^{2}}

= - \frac{2 x ^{2} + 4 x + 5}{2 ( 2 x ^{2} + 6 x + 1 ) ^{2}}

\frac{d}{d x} (3 arcsin (x^{2}))

\int_{1}^{2} 4^{x} d x

a re a 4 x^{2}, \frac{x}{2}

x \to 0 - lim (- x + 3)

\int_{- 1}^{1} π (1 - x^{2}) d x