What is the derivative of # arcsin(x-1)#?

2 Answers
Apr 12, 2018

#1/sqrt(1-(x-1)^2#

Explanation:

derivative of inverse trigonometric functions

the general formula to differentiate the arcsin functions is

#intsin^-1u=1/sqrt(1-u^2)(du)/dx#

#d/dxsin^-1(x-1)=1/sqrt(1-(x-1)^2)*(d(x-1))/dx## "rarr# chain rule

#d/dxsin^-1(x-1)=1/sqrt(1-(x-1)^2)*1#

Apr 13, 2018

#1/(sqrt(1-(x-1)^2)#

Explanation:

We got:

#d/dx(arcsin(x-1))#

Let #y=arcsin(x-1)#

Let's use the chain rule, which states that,

#dy/dx=dy/(du)*(du)/dx#

Let #u=x-1,:.(du)/dx=1#

Then #y=arcsinu,:.dy/(du)=1/(sqrt(1-u^2))#.

Combining,

#dy/dx=1/(sqrt(1-u^2))*1#

#=1/(sqrt(1-u^2))#

Substitute back #u=x-1# to get the final answer:

#=1/(sqrt(1-(x-1)^2)#