Answer
The derivative is $8x-\frac{5}{x^2}$.
Work Step by Step
First, split the numerator to get $h(x)=\frac{4x^3}{x}+\frac{2x}{x}+\frac{5}{x}=4x^2+2+\frac{5}{x}$.
Then, rewrite $h(x)$ as $h(x)=4x^2+2+5x^{-1}$. To differentiate $h(x)$, differentiate the individual terms using the power rule and sum up the results.
The derivative of $4x^2$ is $8x$.
The derivative of $2$ is $0$.
The derivative of $5x^{-1}$ is $(5)(-1)(x^{-1-1})$which simplifies to $-\frac{5}{x^2}$.
Summing everything together gives us $h'(x)=x-\frac{5}{x^2}$.
