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

Answer 1

Paisley Johnson

We could calculate the derivative using the product rule

#(d(f*g))/(dx) = (df)/(dx)* g+f*(dg)/(dx)#

However we can also note that:

#sin(2x)=2sinxcosx#

so:

#f(x) = cos^2(x)sin^2(x) = ((sin2x)/2)^2=1/4sin^2(2x)#

Using the chain rule:

#(d(1/4sin^2(2x)))/dx= 1/4*2sin(2x)cos(x)* 2 = 2sinx * cos x * cos x= 2sinxcos^2x#

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Answer 2

Samantha Adkison

The derivative of ( \cos^2(x)\sin^2(x) ) is ( 2\cos(x)\sin(x)(\sin^2(x) - \cos^2(x)) ).

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Answer from HIX Tutor

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.