What is the derivative of arcsin(4x+2)?

  • Thread starter jumbogala
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In summary, the derivative of arcsin(4x+2) is 4 / (√(1-(4x+2)^2)). The original poster verified their answer using online tools.
  • #1
jumbogala
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Homework Statement


What is the derivative of arcsin(4x+2)?


Homework Equations





The Attempt at a Solution


I just want to check that I'm doing this correctly; my teacher didn't give me any examples to try.

I get 4 / ([tex]\sqrt{1-(4x-2)^2}[/tex])

Is that right?
EDIT: Just realized I posted this in precal math, sorry! =(
 
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  • #2
Why do you have (4x-2) in the radical? Typo, right? Otherwise, it's fine.
 
  • #3
Whoops, it's supposed to say 4x+2. It's still supposed to be in the radical, though.
 
  • #4
Then it's just fine.
 
  • #5

What is the derivative of arcsin(x)?

The derivative of arcsin(x) is equal to 1/sqrt(1-x^2). This can also be written as (1-x^2)^(-1/2).

How do you find the derivative of arcsin(x)?

To find the derivative of arcsin(x), you can use the formula d/dx(arcsin(x)) = 1/sqrt(1-x^2). You can also use the inverse trigonometric identity d/dx(arcsin(x)) = 1/cos(arcsin(x)).

What is the domain of the derivative of arcsin(x)?

The domain of the derivative of arcsin(x) is -1 < x < 1. This is because the derivative is undefined at x = -1 and x = 1 due to the square root in the equation.

How can the derivative of arcsin(x) be used in real-world applications?

The derivative of arcsin(x) can be used in various real-world applications, such as physics and engineering. For example, it can be used to calculate the acceleration of an object moving in a circular path.

Is the derivative of arcsin(x) an odd or even function?

The derivative of arcsin(x) is an odd function. This means that it is symmetric about the origin, and f(-x) = -f(x). This can be seen by substituting -x into the derivative formula, resulting in -(1-(-x)^2)^(-1/2) = -(1-x^2)^(-1/2) = -1/sqrt(1-x^2).

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