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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\int 16 sin^{2} (x co) s^{2} x d x

y^{^{''}} + 4 y = sec^{2} (2 x)

\int 5 tan^{3} (θ) d θ

in v erse l a pl a ce \frac{1}{s ^{2} + s + 1}

\int sin^{2} (\frac{1}{2} x) d x