Using product and chain rules to find derivatives instead of quotient rule

In this example problem, we rewrite a rational function with a negative exponent to avoid using the quotient rule. After doing so, we apply the product rule and chain rule to calculate the first 1st derivative and second 2nd derivative or a function. We then evaluate the first (1st) derivative at a given value of x to determine if the function is increasing or decreasing at the given value of x. We then evaluate the second (2nd) derivative at a given value of x to determine the function's concavity (concave up or concave down) at the given value of x.