How do you find the derivative of #(cos^2(x)sin^2(x))#?
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To find the derivative of ( (\cos^2(x)\sin^2(x)) ), you would use the product rule. Here are the steps:

Identify the functions as u and v: ( u = \cos^2(x) ) and ( v = \sin^2(x) ).

Calculate the derivatives of u and v: ( u' = 2\cos(x)\sin(x) ) and ( v' = 2\sin(x)\cos(x) ).

Apply the product rule formula: ( (uv)' = u'v + uv' ).

Substitute the derivatives and functions: ( (\cos^2(x)\sin^2(x))' = (2\cos(x)\sin(x))(\sin^2(x)) + (\cos^2(x))(2\sin(x)\cos(x)) ).

Simplify the expression to get the final result for ( (\cos^2(x)\sin^2(x))' ).
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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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