BloodyFrozen said:Is that a ##f(y)##? Or like ##f(x) = y =~ ...##
As BloodyFrozen already noted, that should be f(x) = ...SteveM19 said:Homework Statement
This is to help out a 40something calc student -- thank you all in advance for your helpHomework Equations
If f (y) = ln ln ln x, what is ∂y/∂x?
No, it's not right. You have a composite function, y = ln(ln(ln(x))), so you need to use the chain rule a couple of times. It also might be helpful to include parentheses as I did.In response to your other question, you can take y' to be a synonym of dy/dx.SteveM19 said:The Attempt at a Solution
I came up with 1/x, which I got by applying ∂y/∂x ln x = 1/x three times, is this right? Thank you again for your help.
The derivative of ln x is 1/x. This can be derived using the power rule for logarithmic functions.
The derivative of ln x is equal to 1/x because ln x is the inverse function of e^x, and the derivative of e^x is equal to e^x. Using the chain rule, the derivative of ln x can be expressed as 1/x * (1/x), which simplifies to 1/x.
The domain of ln x is all positive real numbers, as the natural logarithm function is only defined for positive values of x. If x is negative, ln x is undefined.
The main difference between ln x and log x is the base of the logarithm. Ln x is the natural logarithm, with a base of e, while log x can have a base of any positive number. Another difference is that ln x is the inverse function of e^x, while log x is the inverse function of the corresponding exponential function with the specified base.
The derivative of ln x can be used to calculate rates of change in many real-world situations, such as population growth, interest rates, and chemical reactions. It can also be used in various fields of science, including physics, biology, and economics, to model and analyze natural phenomena.