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

Lösung

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

\frac{x ^{2} + 4 x + 1}{( x + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 x ( x + 2 ) - 1 \cdot ( x ^{2} - 1 )}{( x + 2 ) ^{2}} : \frac{x ^{2} + 4 x + 1}{( x + 2 ) ^{2}}

= \frac{x ^{2} + 4 x + 1}{( x + 2 ) ^{2}}

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

\frac{\partial}{\partial y} (x^{2} \cdot y^{3})

d er i v a t i v e \frac{4 x ^{3} + 2 x + 5}{x}

x \to 0 lim (\frac{5 ^{x} - 3 ^{x}}{x})

\int (- x^{5} + 6 e^{- 2 x}) d x