Explanation:
we simply use the definitions in the main expression.
f(x) = -3x²
therefore,
f(x + h) = -3(x + h)² = -3(x² + 2hx + h²) = -3x² - 6hx - 3h²
so, we have
((-3x² - 6xh - 3h²) - -3x²)/h
(-3x² - 6xh - 3h² + 3x²)/h
(-6xh - 3h²)/h
this is then
-6x - 3h
and for the limit of h going to 0 this is -6x.