微积分学示例

\frac{{(1 - x^{2})}^{- \frac{1}{2}} sin ({(1 - x^{2})}^{\frac{1}{2}})}{\sqrt{1 - {cos}^{2} ({(1 - x^{2})}^{\frac{1}{2}})}}

$\frac{{(1 - x^{2})}^{- \frac{1}{2}} \sin ({(1 - x^{2})}^{\frac{1}{2}})}{\sqrt{1 - \cos^{2} ({(1 - x^{2})}^{\frac{1}{2}})}}$

解题步骤 1

使用勾股恒等式。

\frac{{(1 - x^{2})}^{- \frac{1}{2}} sin ({(1 - x^{2})}^{\frac{1}{2}})}{\sqrt{{sin}^{2} ({(1 - x^{2})}^{\frac{1}{2}})}}

$\frac{{(1 - x^{2})}^{- \frac{1}{2}} \sin ({(1 - x^{2})}^{\frac{1}{2}})}{\sqrt{\sin^{2} ({(1 - x^{2})}^{\frac{1}{2}})}}$

解题步骤 2

使用负指数规则

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ 将

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

${(1 - x^{2})}^{- \frac{1}{2}}$ 移动到分母。

\frac{sin ({(1 - x^{2})}^{\frac{1}{2}})}{\sqrt{{sin}^{2} ({(1 - x^{2})}^{\frac{1}{2}})} {(1 - x^{2})}^{\frac{1}{2}}}

$\frac{\sin ({(1 - x^{2})}^{\frac{1}{2}})}{\sqrt{\sin^{2} ({(1 - x^{2})}^{\frac{1}{2}})} {(1 - x^{2})}^{\frac{1}{2}}}$

解题步骤 3

假设各项均为正实数，从根式下提出各项。

$\frac{\sin ({(1 - x^{2})}^{\frac{1}{2}})}{\sin ({(1 - x^{2})}^{\frac{1}{2}}) {(1 - x^{2})}^{\frac{1}{2}}}$

解题步骤 4

约去公因数。

$\frac{\sin ({(1 - x^{2})}^{\frac{1}{2}})}{\sin ({(1 - x^{2})}^{\frac{1}{2}}) {(1 - x^{2})}^{\frac{1}{2}}}$

解题步骤 5

重写表达式。

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

$\frac{{(1 - x^{2})}^{- \frac{1}{2}} \sin ({(1 - x^{2})}^{\frac{1}{2}})}{\sqrt[]{1 - \cos^{2} ({(1 - x^{2})}^{\frac{1}{2}})}}$

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微积分学 示例

微积分学示例