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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

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

Vereinfache

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

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

\frac{1}{4} q^{^{''}} + 10 q^{^{'}} + 1000 q = 0

x \to 0 + lim ((1 + x)^{\frac{7}{x}})

\int \frac{2 x ^{5} - 4 x + 8 x}{x} d x

ma c l a u r in ln (1 + e^{x})

\frac{d}{d x} (arcsin (2 x^{4}))