How do you differentiate $y = {cos}^{- 1} (1 - 2 x^{2})$ $y=cos^-1(1-2x^2)$ ?

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How do you differentiate $y = {cos}^{- 1} (1 - 2 x^{2})$ $y=cos^-1(1-2x^2)$ ?

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Answer 1 · 2016-03-06T12:32:03

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

Explanation:

Using the $chain rule$ $color(blue)" chain rule "$

$d/dx[f(g(x)] = f'(g(x)) . g'(x)$

and the standard derivative $d/dx(cos^-1 x) =( -1)/sqrt(1 - x^2)$

$rArr dy/dx = (-1)/sqrt(1 - (1-2x^2)^2) d/dx(1-2x^2)$

$= (4x)/sqrt(1-1 +4x^2 - 4x^4) =( 4x)/sqrt(4x^2(1-x^2))$

$= (4x)/(2xsqrt(1-x^2))= 2/sqrt(1-x^2)$

Answer 2 · 2016-03-06T12:45:37

$d y=(4x)/(1-2x^2)^2 sin^-1(1-2x^2) d x$

Explanation:

$y=cos u" " y^'=- u^' * sin u$
$y=cos^-1(1-2x^2)" "y=cos(1/(1-2x^2))$
$d y=-((0*(1-2x^2)+4x*1)/(1-2x^2)^2)sin(1/(1-2x^2))*d x$
$d y=(4x)/(1-2x^2)^2 sin^-1(1-2x^2) d x$

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How do you differentiate $y = {cos}^{- 1} (1 - 2 x^{2})$ $y=cos^-1(1-2x^2)$ ?

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Explanation:

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How do you differentiate y=cos^-1(1-2x^2)y=cos−1(1−2x2) y=cos^-1(1-2x^2)?

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How do you differentiate $y = {cos}^{- 1} (1 - 2 x^{2})$ $y=cos^-1(1-2x^2)$ ?