derivative of x/(x^{-1+10})

Lösung

\frac{d}{d x} (\frac{x}{x ^{- 1} + 10})

\frac{x ( 10 x + 2 )}{( 1 + 10 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x ^{- 1} + 10})

Wende die Quotientenregel an:

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

= \frac{\frac{d x}{d x} ( x ^{- 1} + 10 ) - \frac{d}{d x} ( x ^{- 1} + 10 ) x}{( x ^{- 1} + 10 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x^{- 1} + 10) = - \frac{1}{x ^{2}}

= \frac{1 \cdot ( x ^{- 1} + 10 ) - ( - \frac{1}{x ^{2}} ) x}{( x ^{- 1} + 10 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x ^{- 1} + 10 ) - ( - \frac{1}{x ^{2}} ) x}{( x ^{- 1} + 10 ) ^{2}} : \frac{x ( 10 x + 2 )}{( 1 + 10 x ) ^{2}}

= \frac{x ( 10 x + 2 )}{( 1 + 10 x ) ^{2}}

\int 2 x - 1 d x

\int t^{3} e^{- 3 t} d t

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

x \to 0 + lim (3 sin (x) ln (x))

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