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What is the derivative of #arctan(x/3)#?

Answer 1

Aurora Alvarado

#d/(dx)[arctanu] = 1/(1+u^2)((du)/(dx))#

#=> 1/(1+x^2/9)*1/3 = 1/(3+x^2/3)#

#= 3/(9+x^2)#

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Answer 2

Christopher Allers

The derivative of ( \arctan(x/3) ) is ( \frac{1}{1+(x/3)^2} ) or ( \frac{3}{x^2+9} ).

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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.

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