How Do You Derive arcsin(e^x)?

[delfam]

Homework Statement

arcsin(e^x)

Homework Equations

arcsin = 1/(1-x^2)^(1/2)

The Attempt at a Solution

f'(x)= 1/(1-x^2)^(1/2) * (e^x) + arcsin(e^x)

I did product rule and got to this but not sure where to proceed after this point.

 

[vela]

Homework Statement

arcsin(e^x)

I take it the problem is to find the derivative of this function.

Homework Equations

arcsin = 1/(1-x^2)^(1/2)

You're being very sloppy here. For one thing, there's no argument for arcsin. But assuming you meant arcsin x, it's still wrong because arcsin x isn't equal to 1/(1-x^2)^(1/2).

I know a lot of students do this and teachers often let them get away with it, but you're really at the point where you need to learn how to write things down using proper notation, if only to be able to communicate clearly with others.

The Attempt at a Solution

f'(x)= 1/(1-x^2)^(1/2) * (e^x) + arcsin(e^x)

I did product rule and got to this but not sure where to proceed after this point.

The original expression isn't the product of two functions, so you shouldn't be using the product rule. You want to use the chain rule here.