derivative of ((5x-3)/(4x-3/x))

Lösung

\frac{d}{d x} (\frac{( 5 x - 3 )}{4 x - \frac{3}{x}})

\frac{- 30 x + 9 + 12 x ^{2}}{( 4 x ^{2} - 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( 5 x - 3 )}{4 x - \frac{3}{x}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 5 x - 3 ) ( 4 x - \frac{3}{x} ) - \frac{d}{d x} ( 4 x - \frac{3}{x} ) ( 5 x - 3 )}{( 4 x - \frac{3}{x} ) ^{2}}

\frac{d}{d x} (5 x - 3) = 5

\frac{d}{d x} (4 x - \frac{3}{x}) = 4 + \frac{3}{x ^{2}}

= \frac{5 ( 4 x - \frac{3}{x} ) - ( 4 + \frac{3}{x ^{2}} ) ( 5 x - 3 )}{( 4 x - \frac{3}{x} ) ^{2}}

Vereinfache

\frac{5 ( 4 x - \frac{3}{x} ) - ( 4 + \frac{3}{x ^{2}} ) ( 5 x - 3 )}{( 4 x - \frac{3}{x} ) ^{2}} : \frac{- 30 x + 9 + 12 x ^{2}}{( 4 x ^{2} - 3 ) ^{2}}

= \frac{- 30 x + 9 + 12 x ^{2}}{( 4 x ^{2} - 3 ) ^{2}}

\frac{d}{d x} (sin^{5} ((x^{2} + 1)^{7}))

\int 6 x cos (x^{2}) d x

\frac{\partial}{\partial x} (x^{8} + 5 x y^{9})

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

\frac{d y}{d x} + x^{2} y = 1