To find the derivative of the function h(x) = (5x + 11)(6x - 24x), we'll use the product rule, which states that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

Let's break down the expression step by step:

h(x) = (5x + 11)(6x - 24x)

Step 1: Expand the expression.
h(x) = (5x + 11)(6x - 24x)
h(x) = 5x * 6x + 5x * (-24x) + 11 * 6x + 11 * (-24x)
h(x) = 30x^2 - 120x^2 + 66x - 264x

Step 2: Simplify the expression.
h(x) = -90x^2 - 198x

Step 3: Find the derivative of h(x).
h'(x) = d/dx(-90x^2 - 198x)

Step 4: Apply the power rule to find the derivative.
h'(x) = -90 * d/dx(x^2) - 198 * d/dx(x)

Step 5: Calculate the derivatives of x^2 and x using the power rule.
h'(x) = -90 * 2x - 198 * 1

Step 6: Simplify the expression.
h'(x) = -180x - 198

The expression for the derivative of h(x) in terms of x is:
h'(x) = -180x - 198