# How do you find the derivative of #f(x)= sin^5 (2x)#?

It is

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To find the derivative of ( f(x) = \sin^5(2x) ), you can use the chain rule. Here's the step-by-step process:

- Start by differentiating the outer function with respect to the inner function.
- Then, multiply by the derivative of the inner function.

Applying this to ( f(x) = \sin^5(2x) ):

- Differentiate the outer function: ( \frac{d}{du}(u^5) = 5u^4 ) where ( u = \sin(2x) ).
- Differentiate the inner function: ( \frac{d}{dx}(2x) = 2 ).

Now, apply the chain rule:

[ f'(x) = 5(\sin(2x))^4 \cdot \cos(2x) \cdot 2 ]

[ f'(x) = 10\sin^4(2x) \cdot \cos(2x) ]

That's the derivative of ( f(x) = \sin^5(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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