derivative of f(x)=sin²x(2x+1)

Question

anonymous · Answer

@Kainui

kainui · Answer

I'm on it!

gorv · Answer

is x(2x+1) are combined in sin 0r only x is there????
@cronch

kainui · Answer

So this looks like a combination of the chain rule and power rule. Show me your best guess @cronch and I'll help you figure out where you're going wrong.

kainui · Answer

It'll be more instructive if you try your best cronch, then once I point out where your mistake is, you won't have to worry about making that type of mistake again. =D

calculusfunctions · Answer

@Kainui  I think @gorv made a good point. Is the question$$f(x) =\sin ^{2}[x(2x +1)]$$OR$$f(x)=(2x +1)\sin ^{2}x$$They are two different functions. @cronch which one are you asked to differentiate?

kainui · Answer

Only time will tell.

anonymous · Answer

I think distributing would be the best thing to do first.

anonymous · Answer

Would make it simpler.

calculusfunctions · Answer

"Only time will tell"?? @Kainui you sound like a fortune cookie lol.

kainui · Answer

Could use a trig identity to make sin^2(whatever) into a simple 1/2-1/2cos(2whatever) which can be foiled and also "easier" I guess. Haha, I'm hungry don't talk about cookies right now.

anonymous · Answer

It's sort of confusing on what the question is as well, if it's the second one that calculusfunctions pointed out then all you have to do is use the product rule really.

calculusfunctions · Answer

Yes @iambatman depending on the intended function, both your suggestions are the most efficient methods.

calculusfunctions · Answer

Apply the distributive property to simplify and then use the chain rule to differentiate, in the first case.  Product rule for the second case.