derivative of 3/(sqrt(1-x^2))

解答

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

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

求解步骤

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

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

\frac{\partial}{\partial x} (\frac{M}{2 p x})

x \to 3 lim (3 x^{4} + 2 x^{2} - 5)

f (x) = (- 3 x^{2} + 2 x + 4)^{12}

\frac{d}{d x} (1 - 169 x^{2} arccos (13 x))

\frac{9 x ^{2} + 9 x}{8 x}