15.
Use the Power Rule to take the derivative of each term. The derivative of
(remember the shortcut that we showed you on this page). The derivative of = 0 (because
the derivative of a constant is zero). Therefore, the derivative is .
16. 0
The derivative of a constant is zero.
- 3 x^2 + 6x + 3
First, expand (x + 1)^3 to get x^3 + 3x^2 + 3x + 1. Now, use the Power Rule to take the derivative
of each term. The derivative of x^3 = 3x^2 . The derivative of 3x^2 = 3(2x) = 6x. The derivative of
3 x = 3. The derivative of 1 = 0 (because the derivative of a constant is zero). Therefore, the
derivative is 3x^2 + 6x + 3.
18.
Use the Power Rule to take the derivative of each term. The derivative of
(remember the shortcut that we showed you on this page). Rewrite as x and as x.
The derivative of x = x . The derivative of x = x . Therefore, the derivative is
= .
- 6 x^2 + 6x − 14
First, expand x(2x + 7)(x − 2) to get x(2x^2 + 3x − 14) = 2x^3 + 3x^2 − 14x. Now, use the Power
Rule to take the derivative of each term. The derivative of 2x^3 = 2(3x^2 ) = 6x^2 . The derivative
of 3x^2 = 3(2x) = 6x. The derivative of 14x = 14. Therefore, the derivative is 6x^2 + 6x − 14.
20.
First, rewrite the terms as . Next, distribute to get: .
