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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (x^{3} y + 12 x^{2} - 64 y)

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

d er i v a t i v e \frac{5 x ^{3}}{( 5 - 3 x ) ^{4}}

d er i v a t i v e f (x) = 5 (x^{3} - x)^{4}

\frac{d}{d x} (\frac{( x - 2 )}{x - 1})