It is very useful for finding derivatives of complicated functions. It will be used later in this chapter to explore more completely the derivatives of functions with complicated exponents. Since y has a derivative from the product rule, we can use implicit differentiation on this last equation to find that derivative. After simplifying, we differentiated the resulting equation implicitly and solved for the derivative. Finally we replaced y with its initial expression to obtain the derivative of y in terms of x.
Exercises VI.B. Find the derivatives of the functions as indicated.
Find the derivatives of the functions as indicated. Find the derivatives of the functions as indicated. Explain your work using first and second derivative analysis. Explain your work using first and second derivative analysis. Explain your work using first and second derivative analysis.