derivative of (x^2/(7+x))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{7 + x})

\frac{14 x + x ^{2}}{( 7 + x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{7 + x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 7 + x ) - \frac{d}{d x} ( 7 + x ) x ^{2}}{( 7 + x ) ^{2}}

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

\frac{d}{d x} (7 + x) = 1

= \frac{2 x ( 7 + x ) - 1 \cdot x ^{2}}{( 7 + x ) ^{2}}

Vereinfache

\frac{2 x ( 7 + x ) - 1 \cdot x ^{2}}{( 7 + x ) ^{2}} : \frac{14 x + x ^{2}}{( 7 + x ) ^{2}}

= \frac{14 x + x ^{2}}{( 7 + x ) ^{2}}

\int \frac{2 x ^{3} - x ^{2} + 4 x - 4}{x ^{4} - 4 x ^{2}} d x

\int_{0}^{2} 1 0^{x} d x

\frac{d}{d x} (e^{3 x} - 1 - 3 x)

d er i v a t i v e f (x) = \frac{2 ( - x ^{2} + 1 )}{( x ^{2} + 1 )}

t an g e n t f (x) = 2 3 x, at x = 64