derivative y=(x^2)/(5-8x)

Lösung

ableitung von

y = \frac{x ^{2}}{5 - 8 x}

\frac{10 x - 8 x ^{2}}{( 5 - 8 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{5 - 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} ) ( 5 - 8 x ) - \frac{d}{d x} ( 5 - 8 x ) x ^{2}}{( 5 - 8 x ) ^{2}}

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

\frac{d}{d x} (5 - 8 x) = - 8

= \frac{2 x ( 5 - 8 x ) - ( - 8 ) x ^{2}}{( 5 - 8 x ) ^{2}}

Vereinfache

\frac{2 x ( 5 - 8 x ) - ( - 8 ) x ^{2}}{( 5 - 8 x ) ^{2}} : \frac{10 x - 8 x ^{2}}{( 5 - 8 x ) ^{2}}

= \frac{10 x - 8 x ^{2}}{( 5 - 8 x ) ^{2}}

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

x \to 0 lim (x^{3} \cdot sin (\frac{1}{x}))

x \to 0 lim ((1 - 2 x)^{\frac{5}{x}})

\int cot^{2} (θ) d θ

d er i v a t i v e y = \frac{4 x ^{2} + 6 x + 8}{x}