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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

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

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

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

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

Multipliziere aus

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

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

d er i v a t i v e f (x) = (8 (x^{3} - 6 x^{2} + 12 x))

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

im pl i c i t \frac{d y}{d x}, 5 x y^{5} + 3 x y = 24

d er i v a t i v e arctan (\frac{x}{6})

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