derivative (8x^2+8x+6)/(sqrt(x))

Lösung

ableitung von

\frac{8 x ^{2} + 8 x + 6}{x}

\frac{12 x ^{2} + 4 x - 3}{x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 6}{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} + 8 x + 6 ) x - \frac{d}{d x} ( x ) ( 8 x ^{2} + 8 x + 6 )}{( x ) ^{2}}

\frac{d}{d x} (8 x^{2} + 8 x + 6) = 16 x + 8

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

= \frac{( 16 x + 8 ) x - \frac{1}{2 x} ( 8 x ^{2} + 8 x + 6 )}{( x ) ^{2}}

Vereinfache

\frac{( 16 x + 8 ) x - \frac{1}{2 x} ( 8 x ^{2} + 8 x + 6 )}{( x ) ^{2}} : \frac{12 x ^{2} + 4 x - 3}{x x}

= \frac{12 x ^{2} + 4 x - 3}{x x}

\frac{d}{d x} (x^{0.15})

\int_{2}^{\infty} e^{- 6 x} d x

y^{^{''}} - 10 y^{^{'}} + 25 y = 30 x + 3

t an g e n t f (x) = \frac{3}{x + 5}, at x = 2

\frac{\partial}{\partial y} (- x - sin (y^{2}))