derivative of 1/(sqrt(9-x^2))

解答

\frac{d}{d x} (\frac{1}{9 - x ^{2}})

\frac{x}{( 9 - x ^{2} ) ^{\frac{3}{2}}}

求解步骤

\frac{d}{d x} (\frac{1}{9 - x ^{2}})

使用指数法则:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((9 - x^{2})^{- \frac{1}{2}})

使用连锁律:

- \frac{1}{2 ( 9 - x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (9 - x^{2})

= - \frac{1}{2 ( 9 - x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (9 - x^{2})

\frac{d}{d x} (9 - x^{2}) = - 2 x

= - \frac{1}{2 ( 9 - x ^{2} ) ^{\frac{3}{2}}} (- 2 x)

化简

- \frac{1}{2 ( 9 - x ^{2} ) ^{\frac{3}{2}}} (- 2 x) : \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{2}}}

= \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{2}}}

in v erse l a pl a ce \frac{1}{( s + 1 ) ^{2} \cdot ( s - 1 )}

h \to 0 lim (\frac{8 ^{h} - 1}{h})

d er i v a t i v e f (x) = \frac{x ^{2} + 2 x - 3}{( x + 1 ) ^{2}}

\int_{- \infty}^{0} \frac{1}{6 - 4 x} d x

y^{^{''}} + 7 y^{^{'}} + 14 y = 1096 e^{2 t} cos (8 t)