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Gercel

Member

Registered: 2009-07-03

Posts: 16

Help FInd derivative of Trig Function

f(x)= sin √ 3x³+3x  (Note its a square root of full function  3x³+3x )

Thats how I solved it.

    f'(x)= Cos(3x³+3x)^½
          = Cos ½(3x³+3x)^-½ × (9x²+3)
          = 9x²+3Cos½ (3x^³+3x)^-½

Did I derive it right??? because solution at the back show that the answer is:

9x^2+3/2 root (3x^2+3x) cos Root (3x^3+3x)

Please Tell me if mines is right or wrong?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help FInd derivative of Trig Function

Hi Gercel;
You can't just say sin(whatever) when differentiated is cos(whatever) which is what you did in the first step. To check it I need something clearer than 9x²+3Cos½ (3x^³+3x)^-½ . What does the Cos1/2 stand for. Please bracket it off better.

Last edited by bobbym (2009-07-05 07:29:54)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Gercel

Member

Registered: 2009-07-03

Posts: 16

Re: Help FInd derivative of Trig Function

First I found the derivative of the outside function Sin and Square root, by moving 1/2 to the front.. Then I did the derivatuve if the inside function 3x³+3x.
Isnt that how Chain rule should work?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help FInd derivative of Trig Function

Hi Gercel;

OK, lets see, 9x²+3Cos½ (3x^³+3x)^-½ what is the first 1/2 here, please use brackets as I don't understand the answer.

I have done the problem so you can check against yours:

Last edited by bobbym (2009-07-05 08:40:25)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Gercel

Member

Registered: 2009-07-03

Posts: 16

Re: Help FInd derivative of Trig Function

Wonderfull, Can you please explain how you got the answer.. please

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Help FInd derivative of Trig Function

To do

Say:

Chain rule is:

Now we can do dy/du but du/dx is hard so we use the chain rule again:

Say:

Chain rule:

so

Now you have du/dx. Now complete the top chain rule:

Last edited by bobbym (2009-07-05 18:37:35)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.