derivative y=(6x^2+6x+2)/(sqrt(x))

Lösung

ableitung von

y = \frac{6 x ^{2} + 6 x + 2}{x}

\frac{9 x ^{2} + 3 x - 1}{x x}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (6 x^{2} + 6 x + 2) = 12 x + 6

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

= \frac{( 12 x + 6 ) x - \frac{1}{2 x} ( 6 x ^{2} + 6 x + 2 )}{( x ) ^{2}}

Vereinfache

\frac{( 12 x + 6 ) x - \frac{1}{2 x} ( 6 x ^{2} + 6 x + 2 )}{( x ) ^{2}} : \frac{9 x ^{2} + 3 x - 1}{x x}

= \frac{9 x ^{2} + 3 x - 1}{x x}

d er i v a t i v e 5 cos (x)

\frac{\partial}{\partial x} (x ln (t))

d er i v a t i v e e^{x} - e^{- x}

\int sin (x) \cdot x d x

\frac{d}{d x} (cos (e^{x^{5} s i n (x)}))