derivative of 3/(x^2+2)

解答

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

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

求解步骤

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

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

\frac{d}{d x} (x - 2 y + 2 z)

\int \frac{3}{1 + x ^{2}} d x

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

t an g e n t f (x) = csc (x), at x = \frac{π}{6}

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