derivative of ((x-5(x^2+5x+25))/(x^3))

Lösung

\frac{d}{d x} (\frac{( x - 5 ) ( x ^{2} + 5 x + 25 )}{x ^{3}})

\frac{375}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x - 5 ) ( x ^{2} + 5 x + 25 )}{x ^{3}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ( x - 5 ) ( x ^{2} + 5 x + 25 ) ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( x - 5 ) ( x ^{2} + 5 x + 25 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} ((x - 5) (x^{2} + 5 x + 25)) = 3 x^{2}

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

= \frac{3 x ^{2} x ^{3} - 3 x ^{2} ( x - 5 ) ( x ^{2} + 5 x + 25 )}{( x ^{3} ) ^{2}}

Vereinfache

\frac{3 x ^{2} x ^{3} - 3 x ^{2} ( x - 5 ) ( x ^{2} + 5 x + 25 )}{( x ^{3} ) ^{2}} : \frac{375}{x ^{4}}

= \frac{375}{x ^{4}}

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

\int \frac{x + 2}{2 x + 1} d x

d er i v a t i v e (\frac{x - 5}{x + 5})^{4}

10 y^{^{''}} + 1000 y = 50 cos (8 t)

\frac{d}{d x} (e^{- x} (1 - x))