Sometimes the relationship between y and x is not explicit; rather, it is implicit. Sometimes the implicit relationship between x and y is complicated. In this case there is absolutely no way to s...Sometimes the relationship between y and x is not explicit; rather, it is implicit. Sometimes the implicit relationship between x and y is complicated. In this case there is absolutely no way to solve for y in terms of elementary functions. The surprising thing is, however, that we can still find y′ via a process known as implicit differentiation.
This page focuses on exercises for finding derivatives of various mathematical functions, emphasizing techniques like logarithmic differentiation and their real-life applications, including population...This page focuses on exercises for finding derivatives of various mathematical functions, emphasizing techniques like logarithmic differentiation and their real-life applications, including population growth and decay modeling. It features the Gompertz growth function with historical NYC population data (1790-1860), detailing the relative rate of change and fitting an exponential curve. A derived model \(p=35741(1.
