derivative of (2+3x/(x^2))

Lösung

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

\frac{- 3 x - 4}{x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{- 3 x - 4}{x ^{3}}

\int sin^{18} (x) cos^{3} (x) d x

d er i v a t i v e g (x) = 4 x^{2} (x^{3} + 5 x)

\int (- 8 sec (x) tan (x) + 5 sec^{2} (x)) d x

\frac{d}{d x} ((2 - 7 x^{\frac{3}{2}})^{2})

y^{^{'}} + e^{x} y = 1