# What is the derivative of #sin^2(x)cos^2(x)#?

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To find the derivative of ( \sin^2(x) \cos^2(x) ), you can use the product rule. The product rule states that if ( f(x) ) and ( g(x) ) are differentiable functions, then the derivative of their product is given by ( (f(x)g(x))' = f'(x)g(x) + f(x)g'(x) ). Applying this rule to ( \sin^2(x) \cos^2(x) ), where ( f(x) = \sin^2(x) ) and ( g(x) = \cos^2(x) ), we get:

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

[ = 2\sin(x)\cos(x)\cos^2(x) - 2\sin^2(x)\cos(x) ]

[ = 2\sin(x)\cos(x)\cos^2(x) - 2\sin^2(x)\cos(x) ]

[ = 2\sin(x)\cos(x)[\cos^2(x) - \sin^2(x)] ]

[ = 2\sin(x)\cos(x)\cos(2x) ]

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