How do you find the derivative of $\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}$ $(1)/((1-x^2)^(1/2))$ ?

Question

How do you find the derivative of $\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}$ $(1)/((1-x^2)^(1/2))$ ?

1 Answer

Impact of this question

4415 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-05T03:25:10

Derivative of $\frac{d}{d x} (\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}) = \frac{x}{{(1 - x^{2})}^{\frac{3}{2}}}$ $color(blue)(d/dx(1/(1-x^2)^(1/2))=x/(1-x^2)^(3/2))$

Explanation:

Start with the given $\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}$ $1/(1-x^2)^(1/2)$

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

$\frac{d}{d x} (\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}) = (- \frac{1}{2}) {(1 - x^{2})}^{- \frac{1}{2} - 1} \cdot \frac{d}{d x} (1 - x^{2})$ $d/dx(1/(1-x^2)^(1/2))=(-1/2)(1-x^2)^(-1/2-1)*d/dx(1-x^2)$

$\frac{d}{d x} (\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}) = (- \frac{1}{2}) {(1 - x^{2})}^{- \frac{3}{2}} \cdot (0 - 2 x)$ $d/dx(1/(1-x^2)^(1/2))=(-1/2)(1-x^2)^(-3/2)*(0-2x)$

$\frac{d}{d x} (\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}) = (- \frac{1}{2}) {(1 - x^{2})}^{- \frac{3}{2}} \cdot (- 2 x)$ $d/dx(1/(1-x^2)^(1/2))=(-1/2)(1-x^2)^(-3/2)*(-2x)$

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

God bless....I hope the explanation is useful.

Science

Math

Humanities

... and beyond

How do you find the derivative of $\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}$ $(1)/((1-x^2)^(1/2))$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the derivative of (1)/((1-x^2)^(1/2))1(1−x2)12(1)/((1-x^2)^(1/2))?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find the derivative of $\frac{1}{{(1 - x^{2})}^{\frac{1}{2}}}$ $(1)/((1-x^2)^(1/2))$ ?