derivative (8x^2+2x+2)/(sqrt(x))

Lösung

ableitung von

\frac{8 x ^{2} + 2 x + 2}{x}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (8 x^{2} + 2 x + 2) = 16 x + 2

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{( 16 x + 2 ) x - \frac{1}{2 x} ( 8 x ^{2} + 2 x + 2 )}{( x ) ^{2}}

Vereinfache

\frac{( 16 x + 2 ) x - \frac{1}{2 x} ( 8 x ^{2} + 2 x + 2 )}{( x ) ^{2}} : \frac{12 x ^{2} + x - 1}{x x}

= \frac{12 x ^{2} + x - 1}{x x}

\int x 7^{x^{2}} d x

y^{^{''}} + 14 \cdot 2 y^{^{'}} + 49 y = 0, y (0) = 0, y^{^{'}} (0) = 1

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

x \to 3 - lim (f (x))

a re a - x^{2}, 3 x - 10, x = 0