We find the derivative using the Quotient Rule, which says that if f(x) = , then f′(x) = . Here, f(x) = , so u = (x + 4)(x − 8) and v = (x + 6)(x − 6). Before we
take the derivative, we can simplify the numerator and denominator of the expression: f(x) = = . Now using the Quotient Rule, we get f(x) = . Next, we don’t simplify. We simply plug in x = 2 to get f(x) =
= = .
11. 106
We find the derivative using the Quotient Rule, which says that if f(x) = , then f′(x) = . We will also need the Chain Rule to take the derivative of the expression in the
denominator. The Chain Rule says that if y = f(g(x)), then y′ = , here, f(x) = , so u = x^6 + 4x^3 + 6 and v = (x^4 - 2)^2 . We get f(x) = . Now we don’t simplify.
We simply plug in x = 1 to getf(x) = = 12.
We find the derivative using the Quotient Rule, which says that if f(x) = , then f′(x) = . Here, f(x) = , so u = x^2 − 3 and v = x − 3. Using the Quotient Rule, we get f′
(x) = . This can be simplified to f′(x) = .