# How do you differentiate #f(x)=-3tan4x^2# using the chain rule?

Pull the constant out front

Simplify

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To differentiate ( f(x) = -3\tan(4x^2) ) using the chain rule:

- Let ( u = 4x^2 ).
- Find ( \frac{du}{dx} = 8x ).
- Find ( \frac{df}{du} = -3\sec^2(u) ).
- Apply the chain rule: ( \frac{df}{dx} = \frac{df}{du} \cdot \frac{du}{dx} ).
- Substitute ( u = 4x^2 ) back into the expression.

The result is ( \frac{df}{dx} = -3 \cdot 8x \sec^2(4x^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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