Question

What is the derivative of `f(x) = arcsin(-10 x - 4)/9`?

Answer 1

`(dy)/(dx)=-10/(9sqrt(1-(10x+4)^2)`

Explanation:

As `y=f(x)=arcsin(-10x-4)/9`

`arcsin(-10x-4)=9y` or `sin(9y)=-10x-4`

i.e. `sin(9y)+10x+4=0`

and differentiating

`9cos(9y)(dy)/(dx)+10=0`

or `(dy)/(dx)=-10/(9cos(9y))`

= `-10/(9sqrt(1-sin^2(9y))`

= `-10/(9sqrt(1-(10x+4)^2)`