How to find derivative of f(x)=(2x^2+1)/(2x^2-1)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to find the derivative of f(x)=(2x^2+1)/(2x^2-1)

We use the quotient rule here, which gives the derivative of f(x)/g(x) as

(f'(x)*g(x)* - f(x)*g'(x))/(g(x))^2

f(x)=(2x^2+1)/(2x^2-1)

f'(x) = [(2x^2+1)'*(2x^2-1) - (2x^2+1)*(2x^2-1)']/(2x^2-1)^2

=> [4x*(2x^2-1) - (2x^2+1)*4x]/(2x^2-1)^2

=>  [8x^2 - 4x - 8x^2 - 4x]/(2x^2-1)^2

=>  -8x/(2x^2-1)^2

The required result is -8x/(2x^2-1)^2

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team