The discussion focuses on deriving the function arcsin(e^x) and highlights the importance of proper notation in calculus. The derivative of arcsin(e^x) requires the application of the chain rule rather than the product rule, as the original expression is not a product of two functions. The correct derivative is f'(x) = e^x / √(1 - (e^x)^2). Participants emphasize the need for clarity in mathematical communication to avoid common mistakes.
PREREQUISITESStudents studying calculus, particularly those focusing on derivatives and inverse functions, as well as educators seeking to improve their teaching of mathematical notation and clarity in communication.
I take it the problem is to find the derivative of this function.delfam said:Homework Statement
arcsin(e^x)
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).Homework Equations
arcsin = 1/(1-x^2)^(1/2)
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.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.