derivative of (x^2/(x^2-16))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 16})

- \frac{32 x}{( x ^{2} - 16 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} - 16})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{2} - 16 ) - \frac{d}{d x} ( x ^{2} - 16 ) x ^{2}}{( x ^{2} - 16 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 16) = 2 x

= \frac{2 x ( x ^{2} - 16 ) - 2 x x ^{2}}{( x ^{2} - 16 ) ^{2}}

Vereinfache

\frac{2 x ( x ^{2} - 16 ) - 2 x x ^{2}}{( x ^{2} - 16 ) ^{2}} : - \frac{32 x}{( x ^{2} - 16 ) ^{2}}

= - \frac{32 x}{( x ^{2} - 16 ) ^{2}}

t an g e n t f (x) = (13 x - 1)^{- \frac{1}{3}}, at x = 5

d er i v a t i v e \frac{t}{( t - 9 ) ^{2}}

25 y^{^{''}} + 30 y^{^{'}} + 9 y = 0

\frac{\partial}{\partial x} (2 x^{0.3} y^{0.3} + 1)

\int \frac{3 x ^{\frac{8}{3}}}{8} + C d x