derivative (x^2)/(5+8x)

Lösung

ableitung von

\frac{x ^{2}}{5 + 8 x}

\frac{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{5 + 8 x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 5 + 8 x ) - \frac{d}{d x} ( 5 + 8 x ) x ^{2}}{( 5 + 8 x ) ^{2}}

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

\frac{d}{d x} (5 + 8 x) = 8

= \frac{2 x ( 5 + 8 x ) - 8 x ^{2}}{( 5 + 8 x ) ^{2}}

Multipliziere aus

2 x (5 + 8 x) - 8 x^{2} : 10 x + 8 x^{2}

= \frac{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}}

d er i v a t i v e f (x) = (x^{5} - x^{3} + 3)

\int \frac{1}{x ( 5 + 3 ln ( x ) )} d x

\int 3^{- 2 x} d x

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

x \to 0 - lim (cos (\frac{1}{x}))