Determine g'(0)?

Question

f(0) = 1

f'(0)=2

g(x)= 1/ (2f(x)-1)³

 

what is g'(0)?

Answer 1

Given g(x) = 1/(2f(x) -1)³, you can find the derivative using the Quotient and/or Chain Rules.

 

Here is the quickest way to do this,

 

g(x) = (2f(x) - 1)^-3 , so

 

g′(x) = (-3)(2f(x) - 1)^-4(2f(x) - 1)′

 

        = (-3)(2f(x) - 1)^-4(2f′(x))

 

        = -6f′(x)/(2f(x) - 1)⁴.

 

To finish the problem, plug in x = 0, and use the other given values f(0) = 1, and f′(0) = 2:

 

g′(0) = -6(2)/(2·1 - 1)⁴ = -12/1 = -12.

 

The answer is -12.