How do you differentiate #y = cos^2 (x^2  3x)#?
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To differentiate ( y = \cos^2(x^2  3x) ), you can use the chain rule. First, differentiate the outer function (\cos^2(u)) with respect to its inner function (u = x^2  3x), and then multiply by the derivative of the inner function.

Differentiate the outer function (\cos^2(u)): [ \frac{d}{du} (\cos^2(u)) = 2\cos(u)\sin(u) ]

Find the derivative of the inner function (u = x^2  3x): [ \frac{du}{dx} = 2x  3 ]

Apply the chain rule: [ \frac{dy}{dx} = 2\cos(x^2  3x)\sin(x^2  3x) \cdot (2x  3) ]
So, the derivative of ( y = \cos^2(x^2  3x) ) is ( 2\cos(x^2  3x)\sin(x^2  3x) \cdot (2x  3) ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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