derivative of (x^2/(x^3+8))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{x ^{3} + 8})

\frac{- x ^{4} + 16 x}{( x ^{3} + 8 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{x ^{3} + 8})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{3} + 8 ) - \frac{d}{d x} ( x ^{3} + 8 ) x ^{2}}{( x ^{3} + 8 ) ^{2}}

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

\frac{d}{d x} (x^{3} + 8) = 3 x^{2}

= \frac{2 x ( x ^{3} + 8 ) - 3 x ^{2} x ^{2}}{( x ^{3} + 8 ) ^{2}}

Vereinfache

\frac{2 x ( x ^{3} + 8 ) - 3 x ^{2} x ^{2}}{( x ^{3} + 8 ) ^{2}} : \frac{- x ^{4} + 16 x}{( x ^{3} + 8 ) ^{2}}

= \frac{- x ^{4} + 16 x}{( x ^{3} + 8 ) ^{2}}

\frac{d}{d x} (103 sin (x) - 10 cos (x))

\int \frac{1}{x ^{2} + 60} d x

x \to \infty lim (4 x e^{(\frac{1}{x})} - 4 x)

t an g e n t f (x) = \frac{3}{x}, at x = 2

a re a y^{2} - 3 x = 4, x - y = 2