The product rule is a fundamental concept in calculus used to compute the derivative of the product of two functions. If you have two functions, $f(x)$ and $g(x)$, the product rule helps you find the derivative of their product

$h(x) = f(x)g(x)$

with respect to $x$. Mathematically, the product rule states that:

$h'(x) = f'(x)g(x) + f(x)g'(x)$

where $h'(x)$ is the derivative of $h(x)$ with respect to $x$, $f'(x)$ is the derivative of $f(x)$ with respect to $x$, and $g'(x)$ is the derivative of $g(x)$ with respect to $x$.

Examples

Find the derivative of the product function $h(x) = (x^2 + 1)(3x - 4)$ with respect to $x$