find the derivative of each function. y =(4x2 - 1)-1/2

Question

Calculus I need to understand the concept to this question please show notes and tips show then I can understand how you came up with the solution.

Answer 1

The function y = (4x² - 1)^-½ has the form y = uⁿ, where u = 4x² - 1 and n = -½.

 

By the chain rule for powers, the derivative of uⁿ is                                              nu^n-1(derivative of u).

 

So, for the given function, y' = -½(4x² - 1)^-3/2(8x)

 

                                                   = -4x/(4x² - 1)^3/2