Math Is Fun Forum

N1

Member

Registered: 2016-08-10

Posts: 3

First year maths

Using the nine yn rules only. Differentiate cos^3x n times

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: First year maths

Hi;

What are the nine yn rules?

To do this requires the chain rule.

Now just plug into A.

manually, using the chain rule and the product rule you can do a few more and play spot the pattern. But, the pattern looks complicated and until you say what the nine yn rules are I can go no further.

Now there is the substitution

so I could start differentiating that n times but I do not know if that is what you want.

---

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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: First year maths

Hi N1,
Are you allowed to use Leibnitz's theorem?
bobbym's second option can give you the answer in compact form.

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: First year maths

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

N1

Member

Registered: 2016-08-10

Posts: 3

Re: First year maths

Thank you everyone.
I found the answer.
Cos^3x=(cos3x +3cosx)/4
1/4 cos3x +3/4 cosx
[yn(nth derivative of y)=a^n cos{ax+b+(nπ/2)}]
.