How do you find the derivative of $arcsin(3x)$ ?

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Answer 1 · 2016-10-03T09:41:29

Derivative of $arcsin(3x)$ is $3/sqrt(1-9x^2)$

Let us first find the derivative of $arcsinx$ and let $y=arcsinx$ ,

Then $x=siny$ and $(dx)/(dy)=cosy=sqrt(1-sin^2y)=sqrt(1-x^2)$

or $(dy)/(dx)=1/sqrt(1-x^2)$ i.e. derivative of $arcsinx$ is $1/sqrt(1-x^2)$

Now using chain rule deivative of $arcsin(3x)$ is

$1/sqrt(1-(3x)^2)xx3=3/sqrt(1-9x^2)$

How do you find the derivative of arcsin(3x)arcsin(3x)?