Inverse Trig Function: Find Derivative of the Function

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?

Dick

What happened to the x??

chapsticks

is it 4/(|4x|(√4x²-1))

I keep getting it wrong

HallsofIvy

What is u in your original integral? What is [itex]u^2[/itex]?

Dick

That's sort of close. But look up the formula again. Isn't the square root part [itex]\sqrt(u^2-1)[/itex] 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?

chapsticks

I mean this one (4x)^2

Dick

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

chapsticks

okay how about this answer??

f'(x)=arcsec4x+ 4/(4x(√(16x)²-1)

chapsticks

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

Attached Thumbnails

 

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?

Dick

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

chapsticks

YAY it finally worked thank you :D