Question

How do I find the derivative of sin2xcos2x using the product rule?

Answer 1

1. \[\cos2x * 2(\cos2x) + (-\sin2x*2)(\sin2x)\]
2. \[2\cos^22x-2\sin^22x\]
3. \[2[\cos^22x-\sin^22x]\]

The answer in the back of the book says it can simplify to 2cos4x. Can someone explain how to do this?

Answer 2

@katlvb21 what calc book do you use ?

Answer 3

im..thinking...chain..rule..then..product...rule..otherwise..you..need...identities..to..go..product..rule..explicitely

Answer 4

@Ephilo Calculus 9th edition by Larson/Edwards

Answer 5

it says we could use trig identities to solve it also, but i'm trying to figure out the product-rule way

Answer 6

oh im using the 8th