derivative of 1/(6+x^2)

解答

\frac{d}{d x} (\frac{1}{6 + x ^{2}})

- \frac{2 x}{( 6 + x ^{2} ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{1}{6 + x ^{2}})

使用指数法则:

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

= \frac{d}{d x} ((6 + x^{2})^{- 1})

使用连锁律:

- \frac{1}{( 6 + x ^{2} ) ^{2}} \frac{d}{d x} (6 + x^{2})

= - \frac{1}{( 6 + x ^{2} ) ^{2}} \frac{d}{d x} (6 + x^{2})

\frac{d}{d x} (6 + x^{2}) = 2 x

= - \frac{1}{( 6 + x ^{2} ) ^{2}} \cdot 2 x

化简

- \frac{1}{( 6 + x ^{2} ) ^{2}} \cdot 2 x : - \frac{2 x}{( 6 + x ^{2} ) ^{2}}

= - \frac{2 x}{( 6 + x ^{2} ) ^{2}}

d er i v a t i v e y = \frac{e ^{x}}{x}

t an g e n t f (x) = x^{4} - 17 x^{2} + 16, at x = 2

a re a - x^{2} + 10, - 10, - 1

\int \frac{1}{sin ^{2} ( x ) \cdot cos ^{2} ( x )} d x

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{e ^{- 3 x}}{x}