derivative of (x^2/(3+8x))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{3 + 8 x})

\frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{3 + 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} ) ( 3 + 8 x ) - \frac{d}{d x} ( 3 + 8 x ) x ^{2}}{( 3 + 8 x ) ^{2}}

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

\frac{d}{d x} (3 + 8 x) = 8

= \frac{2 x ( 3 + 8 x ) - 8 x ^{2}}{( 3 + 8 x ) ^{2}}

Multipliziere aus

2 x (3 + 8 x) - 8 x^{2} : 6 x + 8 x^{2}

= \frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}}

x \cdot y^{^{'}} + y^{2} = 0

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

\int \frac{6}{x ^{6}} d x

\frac{d}{d x} (1 - \frac{4}{x ^{2}})

n = 1 \sum \infty 2^{n} x^{n - 1}