How do you differentiate #sinxcosx#?

Answer 1

# d/dx sinxcosx = cos2x#

Method 1 - Manipulation

# d/dx sinxcosx = d/dx 1/2 sin 2x # # " " = 1/2 d/dx sin 2x # # " " = 1/2 2cos2x # # " " = cos2x #

Method 2: Product Rule

# d/dx sinxcosx = (sinx)(d/dxcosx)+(d/dxsinx)(cosx) # # " " = (sinx)(-sinx)+(cosx)(cosx)# # " " = cos^2x-sin^2x# # " " = cos2x#

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Answer 2

Emma Aldridge

To differentiate sin(x)cos(x), you can use the product rule. The derivative is cos^2(x) - sin^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.

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