Question

find d/dx of f(x) = arcsin(x+1) how would i approach this

Answer 1

just plug in the formula?

Answer 2

yes, just use the formula for the derivative

Answer 3

ty

Answer 4

There is a very useful theorem that says that if you have y= f(x)
and the inverse function x= g(y)
then g'(y)= 1/f'(x)

here y = asin(x-1)
let u= x-1
y= asin(u)
u= sin(y)
du = cos(y) dy
so dy/du = 1/cos(y)
use sin^2(y)+cos^2(y)= 1 to rewrite cos(y) as sqrt(1- sin^2(y))
dy/du= 1/sqrt(1-sin^2(y))
but sin(y)= u, so this is
dy/du = 1/sqrt(1-u^2)

replace u with x-1 to finish this off