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.
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Differentiate the outer function (\cos^2(u)): [ \frac{d}{du} (\cos^2(u)) = -2\cos(u)\sin(u) ]
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Find the derivative of the inner function (u = x^2 - 3x): [ \frac{du}{dx} = 2x - 3 ]
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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 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.
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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