Derivative definition of 3sin2x

[Vilius5234]

Hello, I've watched some videos about derivative definition and especially of trigonometry, but can't seem to get correct answer, I get 3cos2x but the correct answer should be 6cos2x ?
Would be thankfull for full explanation

 

[Deleted member 4993]

Hello, I've watched some videos about derivative definition and especially of trigonometry, but can't seem to get correct answer, I get 3cos2x but the correct answer should be 6cos2x ?
Would be thankfull for full explanation

Have you learned the "chain rule" of differentiation ? You need to use it.

 

[Zermelo]

Well, what do you mean by “derivative definition”? Are you computing the actual limit (which is the definition of the derivative), or are you using formulas (like sin’x = cosx)?
If you are computing the limit, you should show us your work so we can see where you’ve gone wrong, and if you are using the formulas, you probably forgot about the chain rule (as Subhotosh Khan stated)

 

[BigBeachBanana]

There was a similar thread. Study the thread, apply similar ideas and see what you can come up with.

Derivative using limit definition

Find \boxed{\frac{d}{dx}(\sin \sqrt{x})} using the definition of derivative. Hint: Use the following facts \boxed{1)\,\sin(A)-\sin(B)=2\sin\Bigg(\frac{A-B}{2}\Bigg)⋅\cos\Bigg(\frac{A+B}{2}\Bigg)}\\ \boxed{2)\, \lim_{\theta \to 0}\,\frac{\sin\theta}{\theta}=1} What I have so far... \lim_{h \to 0}...

www.freemathhelp.com

 

[Vilius5234]

I mean derivative definition as proving the derivate, here's what I'm working on, and maybe somebody can spot my mistake?

 

[Steven G]

The derivative of the sine of any angle = cos of that same angle times the derivative of that angle.

So what is the angle in sin2x and what is the derivative of that angle?

 

[Vilius5234]

The derivative of the sine of any angle = cos of that same angle times the derivative of that angle.

So what is the angle in sin2x and what is the derivative of that angle?

I understand that sin2x derivative is 2cos2x, but I need to prove it.. I uploaded a picture of my work, after it gets accepted maybe u can help me see the problem

 

[Zermelo]

I mean derivative definition as proving the derivate, here's what I'm working on, and maybe somebody can spot my mistake?

Right on the second line, you state that 3sin2(x +dx) = 3sin(2x)3cos(2dx) … while it is actually 3 ( sin(2x) cos(2dx) +…) aka you have multiplied a factor by 3 two times. I can also see that you are missing a lot of steps, and I recommend doing this derivation step by step, it will be easier both for you and for us! Also, don’t forget to write lim dx->0 at each step!
Note that I wrote dx instead of delta x
Try again and let us know if it goes wrong again so we can check ?

 

[AvgStudent]

There was a similar thread. Study the thread, apply similar ideas and see what you can come up with.

Derivative using limit definition

Find \boxed{\frac{d}{dx}(\sin \sqrt{x})} using the definition of derivative. Hint: Use the following facts \boxed{1)\,\sin(A)-\sin(B)=2\sin\Bigg(\frac{A-B}{2}\Bigg)⋅\cos\Bigg(\frac{A+B}{2}\Bigg)}\\ \boxed{2)\, \lim_{\theta \to 0}\,\frac{\sin\theta}{\theta}=1} What I have so far... \lim_{h \to 0}...

www.freemathhelp.com

Hey, that's my thread LOL ?

 

[Steven G]

I mean derivative definition as proving the derivate, here's what I'm working on, and maybe somebody can spot my mistake?

If the image you sent was orientated correctly, then more helpers will respond.

 

[skeeter]

Derivative definition of 3sin2x

Hello, I've watched some videos about derivative definition and especially of trigonometry, but can't seem to get correct answer, I get 3cos2x but the correct answer should be 6cos2x ? Would be thankfull for full explanation

mathforums.com

 

[Deleted member 4993]

I mean derivative definition as proving the derivate, here's what I'm working on, and maybe somebody can spot my mistake?

You have posted the same problem at multiple site - and at one of those sites you said you solved the problem (yesterday 10 AM). How come you are asking about further explanation here??