- #1
Jan Hill
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Homework Statement
y = 5ln(7lnx)
Homework Equations
y' = 5 x 1/7lnx +97lnx0 x 1/x
= 5(7lnx)/7lnx + 5ln x 7/x
The Attempt at a Solution
y' = 5 + 35ln/x
is this right?
You're completely forgetting the chain rule.Jan Hill said:Homework Statement
y = 5ln(7lnx)
Homework Equations
y' = 5 x 1/7lnx +97lnx0 x 1/x
= 5(7lnx)/7lnx + 5ln x 7/x
Jan Hill said:The Attempt at a Solution
y' = 5 + 35ln/x
is this right?
Yes, but it should be simplified to 5/(x ln(x))Jan Hill said:then I guess it should be
y' = 5/(7lnx) x 7/x
Y' = 35/x(7lnx)
Is that right?
A logarithmic derivative is a mathematical concept used to find the rate of change of a function that is defined in terms of logarithms. It is also known as the log-derivative or the logarithmic differentiation.
A logarithmic derivative is calculated by taking the derivative of the logarithm of a function and then multiplying it by the original function. This can be represented mathematically as (ln f(x))'.
A logarithmic derivative is useful in simplifying complex functions and in solving differential equations. It can also be used to find the relative rates of change between two functions.
Yes, a logarithmic derivative can be negative. This means that the original function is decreasing at a certain point. However, the value of the logarithmic derivative itself does not indicate the direction of the function, as it is dependent on the value of the original function.
Yes, logarithmic derivatives have many real-life applications in fields such as physics, economics, and engineering. For example, they can be used to model population growth, economic growth, and radioactive decay.