derivative of (2-x/(x+1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x + 1) = 1

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

Vereinfache

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

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

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

d er i v a t i v e f (x) = (x + 1)^{3}

(\frac{x ^{2}}{100} + 8 + \frac{20}{x})^{^{'}}

3 y^{^{''}} + 6 y^{^{'}} + 2 y = 0

\int_{1}^{e} \frac{ln ( x )}{x ^{3}} d x