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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int \frac{1}{( y + 2 ) ^{2}} d y

\frac{d y}{d x} + 3 x^{2} y = x

x \to 1 lim (x^{4} - x^{2} + 2)

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

x \to 1 lim (7 x + a)