Question

How do you find the derivative of `y=arcsin(5x+5)`?

Answer 1

Deivative of `arcsin(5x+5)` is `5/sqrt(1-25(x+1)^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(5x+5)` is

`1/sqrt(1-(5x+5)^2)xx5=5/sqrt(1-25(x+1)^2)`