Question

What is the derivative of the function below?

Answer 1

`g(x)=4x-(1)/(4x)=4x-(4x)^(-1)\\\\\\\\g'(x)=\left[4x-(4x)^(-1)\right]'=(4x)'-\left[(4x)^(-1)\right]'=4-[-1(4x)^(-2)]\cdot4\\\\=4+(1)/((4x)^2)\cdot4=4+(4)/(4^2x^2)=\boxed{4+(1)/(4x^2)}\\\\Used:\\\\(f(x)-g(x))'=f'(x)-g'(x)\\\\.[f(g(x))]'=f'(g(x))\cdot g'(x)\\\\(x^n)'=nx^(n-1)`