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

When tackling the derivative of inverse trig functions. I prefer to rearrange and use Implicit differentiation as I always get the inverse derivatives muddled up, and this way I do not need to remember the inverse derivatives. If you can remember the inverse derivatives then you can use the chain rule.

Differentiate Implicitly:

Substituting into [1]

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To find the derivative of ( f(x) = \arctan\left(\frac{x}{\alpha}\right) ), where ( \alpha ) is a constant, use the chain rule:

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

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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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