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How do you find the derivative of #f(x)=arctan(x/a)#?

Answer 1

Scarlett Allison

Using the chain rule:

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

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Answer 2

Christopher Agresta

The derivative of ( f(x) = \arctan(x/a) ) with respect to ( x ) is:

[ f'(x) = \frac{1}{a(1 + (x/a)^2)} ]

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Answer 3

Scarlett Allison

To find the derivative of ( f(x) = \arctan\left(\frac{x}{a}\right) ), where ( a ) is a constant, you can use the chain rule. The derivative is given by:

[ f'(x) = \frac{1}{1 + \left(\frac{x}{a}\right)^2} \cdot \frac{1}{a} = \frac{1}{a(1 + \frac{x^2}{a^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.