# Derivative of Trigonometric Functions

1. Sep 21, 2013

### thatguythere

1. The problem statement, all variables and given/known data
d/dx(sec(x)/1+tan(x)
Evaluate at x=∏/6
2. Relevant equations

3. The attempt at a solution
((1/cos(x))(1+tan(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x))^2

((1/cos(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x))

I used the quotient rule and reduced what I could. Have I done this right and can I go any further before evaluating? Thank you.

2. Sep 21, 2013

### vela

Staff Emeritus
No, that's not correct. Applying the quotient rule involves taking some derivatives. It doesn't appear you've done that.

3. Sep 21, 2013

### thatguythere

Of course I have. 1/cos(x) is the derivative of sec(x) and (sin(x)/cos(x)) is the derivative of (1+tan(x)) are they not?

4. Sep 21, 2013

### vela

Staff Emeritus
No, they're not.

5. Sep 21, 2013

### thatguythere

Right, they are not. Hahaha. Don't mind my red cheeks.

6. Sep 21, 2013

### thatguythere

=((1+tanx)(secxtanx)-(secx)(sec^2x))/(1+tanx)2
=(secxtanx+secxtan^2x-sec^3x)/(1+tanx)2

Is this looking any closer to a correct answer?

7. Sep 21, 2013

### arildno

Yup!

8. Sep 22, 2013

### thatguythere

Is this as far as it goes? Can it be simplified any more?

9. Sep 22, 2013

### Staff: Mentor

I realize that you already recognized that these are wrong, but I thought it worth mentioning why they were wrong.

sec(x) = 1/cos(x) - This is an identity and is how the secant function is defined. It has nothing to do with derivatives.

tan(x) = sin(x)/cos(x) - This is also an identity and is how the tangent function is defined. This is unrelated to derivatives.

10. Sep 22, 2013

### thatguythere

Yes, I was simply confusing myself. As far as my current work, can it be simplified any more?

11. Sep 22, 2013

### Staff: Mentor

You might be able to, but what's the point? Just go ahead and evaluate it now at x = $\pi/6$.

12. Sep 22, 2013

### thatguythere

((2/√3)(√3/3)+((2/√3)(1/3))-(8/3^(3/2)))/(4/3)+((2√3)/3)
=(2/9+2/(3√3)-8/(3^3/2))/((2(2√3+1))/3√3)

13. Sep 22, 2013

### thatguythere

Can anyone tell me if I am on the right track please?

14. Sep 22, 2013

### Staff: Mentor

The above is fine, but what you have below is difficult to read, especially what you have on the right side of the =. Please simplify it.

15. Sep 22, 2013

### thatguythere

Let's try this

#### Attached Files:

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16. Sep 22, 2013

### thatguythere

Oh I guess I could change the term in the denominator to 4/3.

17. Sep 23, 2013

### thatguythere

Bump.

18. Sep 23, 2013

### Staff: Mentor

In the 3rd line of your attachment, the sign of the last term mysteriously changed.