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

Answer 1

Ezekiel Alexander

#d/dx(arctan(x-1))=1/(x^2+2x+2)#

We must first know the derivative of #arctan(x)#, which is:

#d/dxarctan(x)=1/(1+x^2)#

According to the chain rule, we see that

#d/dxarctan(f(x))=1/(1+(f(x))^2)*f'(x)#

So, for #arctan(x-1)#, we see that #f(x)=x-1# and #f'(x)=1#.

#d/dxarctan(x-1)=1/(1+(x-1)^2)*1#

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

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

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Answer 2

Christopher Allers

The derivative of arctan(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.