derivative of (x^2+1/(2x-3))

Lösung

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

\frac{2 x ^{2} - 6 x - 2}{( 2 x - 3 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (2 x - 3) = 2

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

Multipliziere aus

2 x (2 x - 3) - 2 (x^{2} + 1) : 2 x^{2} - 6 x - 2

= \frac{2 x ^{2} - 6 x - 2}{( 2 x - 3 ) ^{2}}

\int \frac{cos ^{2} ( x )}{2} d x

d er i v a t i v e sin^{3} (2 t)

x \to 2 lim (\frac{( x ^{2} - 5 x + 4 )}{x - 2})

\int_{0}^{2} \frac{2 x}{( x ^{2} + 1 ) ^{2}} d x

\frac{\partial}{\partial x} (4 e^{5 x})