derivative. We get f(x) = = . Now we can take thederivative of each term. We get f′(x) = 3x^2 + + 1 − (−3)x−4 = 3x^2 + + 1 + . As wecan see, the second method is a little quicker, and they both give the same result.7.
Here we will find the derivative using the Chain Rule. We will also need the Quotient Rule totake the derivative of the expression inside the parentheses. The Chain Rule says that if y =f(g(x)), then y′ = , and the Quotient Rule says that if f(x) = , then f(x) = . We get f′(x) = 4 . This can be simplified to f′(x) = 4
= .
- 100(x^2 + x)^99 (2x + 1)
Here we will find the derivative using the Chain Rule. The Chain Rule says that if y = f(g(x)),then y′ = . We get f′(x) = 100(x^2 + x)^99 (2x + 1).9.
Here we will find the derivative using the Chain Rule. We will also need the Quotient Rule totake the derivative of the expression inside the parentheses. The Chain Rule says that if y =f(g(x)), then y′ = and the Quotient Rule says that if f(x) = , then f′(x) = . We get f′(x) = . This can be simplified to f′(x) =