Problems

Find the derivative of the given function in Problems 1-21.

1           f(x) = x² 

2           f(t) = t² + 3

3           f(x) = 1 - 2x² 

4           f(x) = 3x² + 2

5           f(t) = 4t

6           f(x) = 2 - 5x

7           f(t) = 4t³

8           f(t)=-t³

9           f(u) = 5√u                                   

10          f(u) =

11          g(x) = x√x

12          g(x) = 1/√x

13          g(t) = t^-2

14          g(t) = t^-3

15          f(y) = 3y^-1 +4y

16          f(y) = 2y³ + 4y²

17          f(x) = ax + b 

18          f(x) = ax²

19          f(x) =

20          f(x) = 1/(x + 2)

21          f(x) = 1/(3 - 2x)

22            Find the derivative of f(x) = 2x² at the point x = 3.

23            Find the slope of the curve f(x) =at the point x = 5.

24            An object moves according to the equation y = 1/(t + 2), t ≥ 0. Find the velocity as a function of t.

25            A particle moves according to the equation y = t⁴. Find the velocity as a function of t.

26            Suppose the population of a town grows according to the equation y = 100t + t². Find the rate of growth at time t = 100 years.

27            Suppose a company makes a total profit of 1000x - x² dollars on x items. Find the marginal profit in dollars per item when x = 200, x = 500, and x = 1000.

28            Find the derivative of the function f(x) = |x + 1|.

29            Find the derivative of the function f(x) = |x³|.

30            Find the slope of the parabola y = ax² + bx + c where a, b, c are constants.