# How do you use the chain rule to differentiate #g(x)=3tan(4x)#?

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To differentiate ( g(x) = 3 \tan(4x) ) using the chain rule, follow these steps:

- Identify the outer function, which is ( \tan(4x) ), and the inner function, which is ( 4x ).
- Find the derivative of the outer function with respect to its inner variable, which is ( \frac{d}{dx}[\tan(u)] = \sec^2(u) \frac{du}{dx} ), where ( u = 4x ).
- Calculate the derivative of the inner function with respect to ( x ), which is simply ( 4 ).
- Substitute the results from steps 2 and 3 into the chain rule formula.
- Multiply the derivative of the outer function by the derivative of the inner function to obtain the derivative of ( g(x) ).

Following these steps, the derivative of ( g(x) ) with respect to ( x ) is:

[ g'(x) = 3 \sec^2(4x) \cdot 4 ]

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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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