# How do you find the derivative of # cos(1-2x)^2#?

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To find the derivative of ( \cos(1-2x)^2 ), you can use the chain rule. The derivative can be calculated as follows:

[ \frac{d}{dx}[\cos(1-2x)^2] = -2 \sin(1-2x) \cdot \frac{d}{dx}(1-2x) ]

Now, differentiate ( 1-2x ) with respect to ( x ):

[ \frac{d}{dx}(1-2x) = -2 ]

Putting it back into the expression:

[ \frac{d}{dx}[\cos(1-2x)^2] = -2 \sin(1-2x) \cdot (-2) ]

[ = 4 \sin(1-2x) ]

So, the derivative of ( \cos(1-2x)^2 ) with respect to ( x ) is ( 4 \sin(1-2x) ).

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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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