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.
A derivative inverse function is a mathematical concept in calculus that represents the inverse of a derivative function. It is a function that, when applied to the output of the original derivative function, yields the original input.
A derivative inverse function is calculated by finding the inverse of the original function and then finding the derivative of that inverse function. This can be done using the chain rule in calculus.
The purpose of a derivative inverse function is to help us understand the relationship between a function and its inverse. It can also be used to find the rate of change of a function at a specific point.
No, a derivative inverse function may not exist for all functions. It depends on the properties of the original function and whether it is invertible or not. In general, a function must be one-to-one and onto for its inverse to exist.
A derivative inverse function has many real-life applications, such as in physics, economics, and engineering. It can be used to solve optimization problems, calculate velocity and acceleration, and analyze the relationship between variables in a system.