# How do you find the derivative of #cos^2x sinx#?

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The derivative can be written in different ways.

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To find the derivative of ( \cos^2(x) \sin(x) ), we can use the product rule. The product rule states that if you have two functions, ( u(x) ) and ( v(x) ), then the derivative of their product is given by ( u'(x)v(x) + u(x)v'(x) ).

So, let's apply the product rule to ( \cos^2(x) ) and ( \sin(x) ):

( u(x) = \cos^2(x) )

( v(x) = \sin(x) )

Now, we find the derivatives:

( u'(x) = -2\cos(x)\sin(x) )

( v'(x) = \cos(x) )

Finally, applying the product rule formula:

( \frac{d}{dx} (\cos^2(x) \sin(x)) = -2\cos(x)\sin^2(x) + \cos^3(x) \sin(x) )

So, the derivative of ( \cos^2(x) \sin(x) ) is ( -2\cos(x)\sin^2(x) + \cos^3(x) \sin(x) ).

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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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