derivative of (3x(4-x)/(5x^2))

Lösung

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

- \frac{12}{5 x ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{3}{5} \cdot \frac{( 4 - 2 x ) x ^{2} - 2 xx ( 4 - x )}{( x ^{2} ) ^{2}} : - \frac{12}{5 x ^{2}}

= - \frac{12}{5 x ^{2}}

x \to 0 lim (\frac{sin ( 3 x )}{x} + 2)

\frac{1}{x ^{4}} \frac{d y}{d x} = 19 + 15 y

\frac{d ^{2}}{d x ^{2}} (t^{3} (e)^{3 t})

\int (t^{2} + 1) e^{- 2 t} d t

t an g e n t y = 4 sin (x) cos (x), at x = \frac{π}{4}