Inverse Trig Function: Find Derivative of the Function

In summary, the conversation is discussing finding the derivative of the function f(x)=arcsec(4x). The relevant equation is d/dx[arcsecu]=u'/(|u|(√u2-1). The attempt at a solution includes using the formula to get f'(x)=1/√15, but the person keeps getting it wrong in their online homework. After some back and forth, they realize their mistake and correctly solve the problem as f'(x)=1/(4x√(16x^2-1)).
  • #1
chapsticks
38
0

Homework Statement


find the derivative of the function
f(x)=arcsec(4x)


Homework Equations


I think this is a Relevant equations.

d/dx[arcsecu]=u'/(|u|(√u2-1)


The Attempt at a Solution


f'(x)=4/(|4|(√42-1)
=1/√15

I keep getting wrong in my online homework why? :confused:
 
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  • #2
chapsticks said:

Homework Statement


find the derivative of the function
f(x)=arcsec(4x)


Homework Equations


I think this is a Relevant equations.

d/dx[arcsecu]=u'/(|u|(√u2-1)


The Attempt at a Solution


f'(x)=4/(|4|(√42-1)
=1/√15

I keep getting wrong in my online homework why? :confused:

What happened to the x??
 
  • #3
is it 4/(|4x|(√4x2-1))

I keep getting it wrong
 
  • #4
What is u in your original integral? What is [itex]u^2[/itex]?
 
  • #5
chapsticks said:
is it 4/(|4x|(√4x2-1))

I keep getting it wrong

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?
 
  • #6
I mean this one (4x)^2
 
  • #7
chapsticks said:
I mean this one (4x)^2

Ok, then keep writing it like that. And what about my other question?
 
  • #8
okay how about this answer??

f'(x)=arcsec4x+ 4/(4x(√(16x)2-1)
 
  • #9
I did this one in my homework online and it keeps saying I'm wrong
 

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  • #10
chapsticks said:
okay how about this answer??

f'(x)=arcsec4x+ 4/(4x(√(16x)2-1)

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

That looks right, except you have x instead of |x|.
 
  • #12
YAY it finally worked thank you :D
 

1. What is the definition of an inverse trig function?

An inverse trig function is a mathematical function that returns the angle whose trigonometric ratio matches the input value. It is the opposite of a regular trig function, which takes an angle as input and returns a trigonometric ratio as output.

2. How do you find the derivative of an inverse trig function?

To find the derivative of an inverse trig function, you can use the chain rule. First, rewrite the function using the inverse trig identity. Then, take the derivative of the inner function and multiply it by the derivative of the inverse trig function.

3. What is the derivative of inverse sine (arcsin) function?

The derivative of inverse sine (arcsin) function is equal to 1 divided by the square root of 1 minus the input value squared. This can also be written as 1/sqrt(1-x^2).

4. How do you find the derivative of inverse tangent (arctan) function?

The derivative of inverse tangent (arctan) function is equal to 1 divided by 1 plus the input value squared. This can also be written as 1/(1+x^2).

5. Can the derivative of an inverse trig function be negative?

Yes, the derivative of an inverse trig function can be negative. It depends on the input value and the specific inverse trig function being used. For example, the derivative of inverse sine can be negative for certain input values between -1 and 1.

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