derivative (8x^2+8+4)/(sqrt(x))

Lösung

ableitung von

\frac{8 x ^{2} + 8 + 4}{x}

\frac{12 x ^{2} - 6}{x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x ^{2} + 8 + 4}{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 + 4 ) x - \frac{d}{d x} ( x ) ( 8 x ^{2} + 8 + 4 )}{( x ) ^{2}}

\frac{d}{d x} (8 x^{2} + 8 + 4) = 16 x

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

= \frac{16 x x - \frac{1}{2 x} ( 8 x ^{2} + 8 + 4 )}{( x ) ^{2}}

Vereinfache

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

= \frac{12 x ^{2} - 6}{x x}

\int (x + 5) 10 x + x^{2} d x

t an g e n t f (x) = x + \frac{4}{x}, (4, 5)

\frac{\partial}{\partial x} (y sin (x y))

\frac{d y}{d x} = \frac{9 x ^{2} - 6}{x ^{2}}

\frac{\partial}{\partial y} (x e^{y} - x^{5} + y - 3)