Q. Let $f$ be a derivable function on $R$ such that its derivative function is given by $f^{\prime}(x)=$ $\frac{4 x^2-x^4-1}{2\left(x^4+1\right)}$, then
Application of Derivatives
Solution:
$f ^{\prime}( x )=\frac{2 x ^2}{\left(1+ x ^4\right)}-\frac{1}{2}$
Let $ g(x)=\frac{2 x^2}{1+x^4}$
then $ g^{\prime}(x)=\frac{-4 x(x-1)(x+1)}{\left(1+x^4\right)^2}$
