# How do you differentiate #g(x)= 3tan4x *sin2x*cos2x# using the product rule?

The rule is very simple, you derive one function and leave the others untouched, and then sum all these terms. So:

We can readjust the three terms:

The result will be the sum of the three terms.

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To differentiate ( g(x) = 3\tan(4x) \cdot \sin(2x) \cdot \cos(2x) ) using the product rule:

- Identify the functions ( f(x) = 3\tan(4x) ), ( h(x) = \sin(2x) ), and ( k(x) = \cos(2x) ).
- Apply the product rule: ( g'(x) = f'(x) \cdot h(x) \cdot k(x) + f(x) \cdot h'(x) \cdot k(x) + f(x) \cdot h(x) \cdot k'(x) ).
- Find the derivatives of each function using standard differentiation rules.
- Substitute the derivatives and original functions into the product rule formula to find ( 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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