Cracking The Ap Calculus ab Exam 2018

Chapter 6 Differentiability ...

In calculus, you’ll be asked to do two things: differentiate and integrate. In this section, you’re going ...

Rule No. 1: If y = xn, then = nxn-1 That’s it. Wasn’t that simple? Of course, this and all of the fo ...

Rule No. 3: If y = kx, then = k (where k is a constant) Rule No. 4: If y = k, then = ...

Example 13: If y = 3x^4 + 8x^10 , then = 12x^3 + 80x^9. Example 14: If y = 7x−4 + 5x − , then ...

Generally, you’ll have to take only first and second derivatives. Notice how we simplified the derivatives in ...

PRACTICE PROBLEM SET 4 Find the derivative of each expression and simplify. The answers are in Chapter 19. 1.(4x^ ...

16. 0 17.(x + 1)^3 18. 19.x(2x + 7)(x − 2) 20. THE PRODUCT RULE Now that you know how to find derivatives o ...

doesn’t matter. It does matter with other rules, though, so it helps to use the same order each time. If ...

You could also write f(x) = as f(x) = u Then you could derive the Quotient Rule using the Prod ...

Example 6: In order to take the derivative of , you have to use the Chain Rule. THE CHAIN RULE The most im ...

y = (g)^5 , so = 5(g)^4 , where g = 5x^3 + 3x Then we multiplied by the derivative of g: (15x^ ...

If y = y(v) and v = v(x), then As you can see, these grow quite complex, so we simplify these ...

PROBLEM 5. Find if y = . Answer: = = PROBLEM 6. Find if y = . Answer: = = PR ...

Simplify when possible. The answers are in Chapter 19. 1.Find f′(x) if f(x) = . 2.Find f′(x) if f(x) = ...

16.Find if y = u^2 − 1 and u = . 17.Find at x = 1 if y = and t = x^3. 18.Find i ...

Next, rewrite this as Next, use some of the trigonometric limits that you memorized back in Chapter 3. S ...

Example 2: Find the derivative of . Use the Quotient Rule. Because = tan x, you should get tan x = sec^ ...

sec x = sec x tan x Example 5: Find the derivative of . You get the idea by now. Because = csc x, you ...

Here are some solved problems. Do each problem, covering the answer first, then checking your answ ...