# How do you differentiate #y=tan^-1(5x)#?

substitute results into (A) and change u back into terms of x.

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To differentiate ( y = \tan^{-1}(5x) ), you can use the chain rule of differentiation. The derivative is:

[ \frac{dy}{dx} = \frac{1}{1 + (5x)^2} \cdot 5 ]

or simplified as:

[ \frac{dy}{dx} = \frac{5}{1 + 25x^2} ]

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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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