derivative of (x^2+2x/(4-5x))

Lösung

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

\frac{- 5 x ^{2} + 8 x + 8}{( 4 - 5 x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( 2 x + 2 ) ( 4 - 5 x ) - ( - 5 ) ( x ^{2} + 2 x )}{( 4 - 5 x ) ^{2}} : \frac{- 5 x ^{2} + 8 x + 8}{( 4 - 5 x ) ^{2}}

= \frac{- 5 x ^{2} + 8 x + 8}{( 4 - 5 x ) ^{2}}

t an g e n t f (x) = tan (x), at x = \frac{π}{4}

x \to 0 lim (\frac{cos ( 7 x ) tan ( 7 x )}{x})

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

x \to 3 lim (\frac{( x ^{4} - 81 )}{x - 3})

d er i v a t i v e f (x) = (x^{5} - 4 x^{3} - 7)^{8}