derivative of (x^2+5x-1/(x^2))

Lösung

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

\frac{- 5 x + 2}{x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + 5 x - 1 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{2} + 5 x - 1 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{2} + 5 x - 1) = 2 x + 5

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

= \frac{( 2 x + 5 ) x ^{2} - 2 x ( x ^{2} + 5 x - 1 )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{( 2 x + 5 ) x ^{2} - 2 x ( x ^{2} + 5 x - 1 )}{( x ^{2} ) ^{2}} : \frac{- 5 x + 2}{x ^{3}}

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

d er i v a t i v e - 3 + 12 x - 3 x^{2}

s l o p e in t erce pt - 6 x = 10 - y - 36 x = 48 - 6 y

\int 4 cos^{2} (x) tan^{3} (x) d x

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 x} ln (x)

d er i v a t i v e 1 - 6 x