Question

find the derivative of f(x)= 12cosxsinx

Answer 1

Use the product rule here.

Answer 2

12 cos 2x

Answer 3

would the answe be 12cos^2xsin^2x?

Answer 4

first, better convert 12cosxsinx to 6sin2x next find its derivative

Answer 5

Almost gnarballs, the answer is really close to that though, don't listen to these guys, they're giving poor advice.

Answer 6

well since the d of cos is -sin would the whole thing be negative?

Answer 7

So the derivative of cosxsinx is 12[(-sinx)(sinx)+(cosx)(cosx)] and I left it this way to show you how the product rule is used.

Answer 8

So you can see it simplifies to 12cos^2x-12sin^2x, yes? You were nearly correct.

Answer 9

oh the twelve distributes to both parts ! of course.... the program did not like that answer though

Answer 10

\[\large{ f(x)= 12 \cdot \cos x \cdot\sin x}\]

\[\large{ f'(x)= {d\over dx}(12 \cdot \cos x \cdot \sin x) \\
f'(x)= 12\cdot {d\over dx}(\cos x \cdot \sin x) \\
f'(x)= 12\cdot \left( (\cos x)'(\sin x) + (\cos x)(\sin x)' \right) }\]

Answer 11

It appears as though it simplifies with a trigonometric identity further http://www.wolframalpha.com/input/?i=d%2Fdx%2012cosxsinx&t=crmtb01

Answer 12

no luck

Answer 13

Oh right, this identity.

http://www.youtube.com/watch?v=IaZFDmVtyyU

Answer 14

Perhaps the program you're typing into doesn't like the notation of squaring sine and cosine like that. Try:

12(cosx)^2-12(sinx)^2

Answer 15

wow its my fault i changed it to x to post here, so i used x to answer it, while the constant they use is q ! thank you very much guys

Answer 16

lol Thankfully no trig identities needed, although they make it look nicer they tend to over complicate things sometimes.