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How do you find the derivative of #tan^-1(x)#?

Answer 1

Ezekiel Alexander

# (dy)/(dx)=1/(1+x^2)# Let

#y=tan^-1(x)#

#tany=x#

Differentiating both sides with respect to 'x'

#sec^2y(dy)/(dx)=1#

# (dy)/(dx)=1/(sec^2y)# As

#sec^2=1+tan^2y#

So,

# (dy)/(dx)=1/(1+tan^2y)#

# (dy)/(dx)=1/(1+x^2)#

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Answer 2

Aurora Alvarado

To find the derivative of ( \tan^{-1}(x) ), use the formula ( \frac{d}{dx}(\tan^{-1}(x)) = \frac{1}{1+x^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.

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