Inverse Trig Function: Find Derivative of the Function

1. Jan 19, 2012

chapsticks

1. The problem statement, all variables and given/known data
find the derivative of the function
f(x)=arcsec(4x)

2. Relevant equations
I think this is a Relevant equations.

d/dx[arcsecu]=u'/(|u|(√u2-1)

3. The attempt at a solution
f'(x)=4/(|4|(√42-1)
=1/√15

I keep getting wrong in my online homework why?

2. Jan 19, 2012

Dick

What happened to the x??

3. Jan 20, 2012

chapsticks

is it 4/(|4x|(√4x2-1))

I keep getting it wrong

4. Jan 20, 2012

HallsofIvy

Staff Emeritus
What is u in your original integral? What is $u^2$?

5. Jan 20, 2012

Dick

That's sort of close. But look up the formula again. Isn't the square root part $\sqrt(u^2-1)$ instead of what you have? And when you write something like 4x^2 it's not clear whether you mean (4x)^2 or 4*(x^2). Which do you mean?

6. Jan 20, 2012

chapsticks

I mean this one (4x)^2

7. Jan 20, 2012

Dick

Ok, then keep writing it like that. And what about my other question?

8. Jan 20, 2012

chapsticks

f'(x)=arcsec4x+ 4/(4x(√(16x)2-1)

9. Jan 20, 2012

chapsticks

I did this one in my homework online and it keeps saying I'm wrong

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10. Jan 20, 2012

Dick

Stop changing things without giving any reason. Why did you put the arcsec4x in there? Why did you drop the absolute value on |4x|? (4x)^2 was right, (16x)^2 isn't. Why not?

11. Jan 20, 2012

Dick

That looks right, except you have x instead of |x|.

12. Jan 20, 2012

chapsticks

YAY it finally worked thank you :D