# How do you find the derivative of #y = sin(tan 2x)#?

The chain rule must be applied, which implies that

Regarding you, we have:

These functions, when entered into the original formula, yield:

After dividing the three, you obtain

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To find the derivative of ( y = \sin(\tan(2x)) ), you can use the chain rule. Here's the process:

- Identify the outer function as (\sin(u)) and the inner function as (\tan(2x)).
- Find the derivative of the outer function with respect to its inner function: (\frac{d}{du}[\sin(u)] = \cos(u)).
- Find the derivative of the inner function with respect to (x): (\frac{d}{dx}[\tan(2x)] = 2\sec^2(2x)).
- Apply the chain rule: Multiply the derivative of the outer function by the derivative of the inner function.
- Substitute the inner function back into the result.

Therefore, the derivative of ( y = \sin(\tan(2x)) ) with respect to (x) is:

[ y' = \cos(\tan(2x)) \cdot 2\sec^2(2x) ]

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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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