derivative of (x^2/(1+8x))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{1 + 8 x})

\frac{2 x + 8 x ^{2}}{( 1 + 8 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{1 + 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} ) ( 1 + 8 x ) - \frac{d}{d x} ( 1 + 8 x ) x ^{2}}{( 1 + 8 x ) ^{2}}

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

\frac{d}{d x} (1 + 8 x) = 8

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

Multipliziere aus

2 x (1 + 8 x) - 8 x^{2} : 2 x + 8 x^{2}

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

in v erse l a pl a ce \frac{s}{s ^{2} - 9}

\int_{0}^{1} - e^{- x} d x

\frac{d y}{d x} = 2 x + 3

x \to 0 - lim (\frac{2}{3 x ^{\frac{1}{3}}})

\int tan (4 θ) d θ