derivative (x^2)/(x-3)

Lösung

ableitung von

\frac{x ^{2}}{x - 3}

\frac{x ^{2} - 6 x}{( x - 3 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x - 3) = 1

= \frac{2 x ( x - 3 ) - 1 \cdot x ^{2}}{( x - 3 ) ^{2}}

Vereinfache

\frac{2 x ( x - 3 ) - 1 \cdot x ^{2}}{( x - 3 ) ^{2}} : \frac{x ^{2} - 6 x}{( x - 3 ) ^{2}}

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

y^{^{''}} + 4 y^{^{'}} + 4 y = x^{2}

\int (8 x^{5} - 5 x^{4} - 4 x^{3} - 6 x^{2} - 2 x - 3) d x

d er i v a t i v e \frac{30000}{1.8 t + 9}

\int \frac{1}{4 - 3 x} d x

s l o p e (2.5) (- 1.7)