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

Answer 1

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

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)#
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Answer 2

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

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#
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Answer 3

The derivative of arcsin(x-1) is 1 / √(1 - (x-1)^2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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