Finding derivative of arcsin(√x)?

[christinee112]

Homework Statement

Finding the derivative of f(x):

f(x)=arcsin(√x)

Homework Equations

f(x)=arcsin
f'(x)=1/(√1-x²)

The Attempt at a Solution

1/√(1-x²)*1/2x^-1/2

Or would I be doing the product rule?

 

[tiny-tim]

welcome to pf!

hi christinee112! welcome to pf!

[1/√(1-x²)*1/2x^-1/2

Or would I be doing the product rule?

no, your chain rule method is correct,

but you've confused yourself by using "x" to mean two different things! ​

 

[christinee112]

hi christinee112! welcome to pf!


no, your chain rule method is correct,

but you've confused yourself by using "x" to mean two different things! ​

Thank you!
However, I'm not sure what you mean by when you say that I am using "x" to mean two different things?

Would I not take the derivative of √x after finding the derivative of arcsin?

 

[tiny-tim]

f'(√x) = (√x)'/√(1 - (√x)²)