Question

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

Answer 1

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

Explanation:

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)`