Math Is Fun Forum

Gercel

Member

Registered: 2009-07-03

Posts: 16

HELP Find Derivative of a Trigonometric Function

Hi,
I need to find a Derivative of a drigonometric function.

1.         F(x)= sin x sec x
  That how i did it:  f'(x)= Cos x Sec x Sec x Tan x Sin

But the answer shows f'(x)= Sec² x

         Question: Is mine wrong or is the answer wrong? Please explain how to do it.
Thank you)

Also, how to solve this type of derivative

1/Sec x Tan X

Can anybody solve it for me, please and explain.
Thank you

Last edited by Gercel (2009-07-05 04:06:22)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: HELP Find Derivative of a Trigonometric Function

Hi Gercel;

For #1;

The book answer is right, here's why:

By the product rule:

Now remember:

Last edited by bobbym (2009-07-05 04:57:09)

---

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 a Trigonometric Function

hmm, what about
Sinx Secx
Sin x will be u                u'v+uv'
Sec x will be v               Cos x (Sec x) + Sin x (Sec x Tanx)
                              After that I dont know how yo simplified to   Tan x^2 +1 and got sec ^2 x

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: HELP Find Derivative of a Trigonometric Function

Hi Gercel;

is one that I just know. But it is easy to prove.

Last edited by bobbym (2009-07-05 05:06:10)

---

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 a Trigonometric Function

One more question, when I do derivatives do I always have to put d/dx, dx/dy or I can simply put f '(x)  in front and do the derivative without d/dx or dy/dx

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: HELP Find Derivative of a Trigonometric Function

Hi Gercel;

Yes, f'(x) is the same as dy/dx.

Here's how to use the trig subs on  problem #1:

OK, what else is there? I am losing my way.

Last edited by bobbym (2009-07-05 05:25:37)

---

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 a Trigonometric Function

I kind of understood it.)) Thankx