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

Lösung

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

\frac{- x + 7}{( x + 3 ) ^{3}}

Schritte zur Lösung

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

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

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

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

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

Vereinfache

\frac{1 \cdot ( x + 3 ) ^{2} - 2 ( x + 3 ) ( x - 2 )}{( ( x + 3 ) ^{2} ) ^{2}} : \frac{- x + 7}{( x + 3 ) ^{3}}

= \frac{- x + 7}{( x + 3 ) ^{3}}

\int \frac{12}{x ^{2} - 9} d x

\frac{d}{d x} (\frac{1 + csc ( x ^{5} )}{1 - cot ( x ^{5} )})

\int \frac{y ^{3}}{3} d y

\frac{\partial}{\partial x} (2 y arctan (\frac{x}{y}))

\int sin (x - 2) d x