SOLUTION: Let f(x) = (4x^2)-7))/(x^2+1) Then, f'(2) = ? Please explain Thank you

Algebra ->  Equations -> SOLUTION: Let f(x) = (4x^2)-7))/(x^2+1) Then, f'(2) = ? Please explain Thank you      Log On


   

Question 991663: Let f(x) = (4x^2)-7))/(x^2+1)
Then,
f'(2) = ?

Please explain
Thank you
Answer by satyareddy22(84) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = (4x^2)-7))/(x^2+1)
Differentiating
f'(x)=[(x^2+1)d/dx(4x^2)-7)-(4x^2)-7)d/dx(x^2+1)]/(x^2+1)^2
f'(x)=[(x^2+1)(8x)-(4x^2)-7)(2x)]/(x^2+1)^2
f'(x)=[8x^3+8x-8x^3+14x]/(x^2+1)^2
f'(x)=22x/(x^2+1)^2
Now ,
f'(2)=22*2/(2^2+1)^2=44/5^2=44/25
f'(2)=44/25