How do you find the derivative of $arcsin(5x)$ ?

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Answer 1 · 2018-04-17T09:59:50

$y'=5/sqrt(1-(5x)^2)$

$y=sin^-1(5x)$

Substitute for $x$

$sinu=5x$

$cosu*du=5dx$

$(du)/dx=5/cosu$ $color(green)(rarr(1)$

After substitution,

$y=sin^-1sinu$

$color(blue)(sin^-1sinu=u$

$y=u$

Differentiate with respect to $x$

$y'=(du)/dx$

Substitute from $color(green) ((1)$

$y'=5/cosu$

$y'=5/sqrt(1-sin^2u)$

**Reverse the substitution **

$y'=5/sqrt(1-(5x)^2)$

$color(red) "and the general formula to find the derivative of arcsin functions"$

$color(green)(d/dxsin^-1u=1/sqrt(1-u^2)(du)/dx$

How do you find the derivative of arcsin(5x)arcsin(5x)?