# How do you differentiate #g(x) = sqrt(x-3)tanx# using the product rule?

Sort the products into f and g, identify their derivatives, then enter all of that information into the product rule to make things simpler.

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To differentiate ( g(x) = \sqrt{x-3} \tan(x) ) using the product rule, you can follow these steps:

- Identify the two functions being multiplied: ( f(x) = \sqrt{x-3} ) and ( h(x) = \tan(x) ).
- Apply the product rule: ( g'(x) = f'(x)h(x) + f(x)h'(x) ).
- Find the derivatives of each function:
- ( f'(x) ) is the derivative of ( \sqrt{x-3} ).
- ( h'(x) ) is the derivative of ( \tan(x) ).

- Substitute the derivatives and the original functions into the product rule formula.
- Simplify the expression to get the derivative ( g'(x) ).

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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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