derivative (x^2)/(5+4x)

Lösung

ableitung von

\frac{x ^{2}}{5 + 4 x}

\frac{10 x + 4 x ^{2}}{( 5 + 4 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{5 + 4 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 + 4 x ) - \frac{d}{d x} ( 5 + 4 x ) x ^{2}}{( 5 + 4 x ) ^{2}}

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

\frac{d}{d x} (5 + 4 x) = 4

= \frac{2 x ( 5 + 4 x ) - 4 x ^{2}}{( 5 + 4 x ) ^{2}}

Multipliziere aus

2 x (5 + 4 x) - 4 x^{2} : 10 x + 4 x^{2}

= \frac{10 x + 4 x ^{2}}{( 5 + 4 x ) ^{2}}

a re a e^{x}, e^{- 3 x}, ln (4)

\frac{d x}{d t} = 1 - x^{2}

\frac{d}{d x} (\frac{3 ( x ^{2} + 2 ) ^{3}}{5})

\frac{d x}{d t} = a x

t an g e n t \frac{( x + 1 )}{( x ^{2} + x + 1 )}