Cracking The Ap Calculus ab Exam 2018

10. We find the derivative of a function, f(x), using the definition of the derivative, which is f′(x) = ...

can cancel the h in the numerator and the denominator to get f′(8) = . Now, we take the limit: f′(8) = ...

. Now we can factor out the h from the numerator and cancel it with the h in the denominator: f′(x) = ...

= . This simplifies to f′(x) = = . Now we can cancel the factor h in the numerator and the deno ...

Simply use the Power Rule. The derivative is 11x^7 = 11(7x^6 ) = 77x^6. 54 x^2 + 12 Use the Power Rule ...

this page). Therefore, the derivative is −42x−8 − . 10. Use the Power Rule to take the derivative of each ...

15. Use the Power Rule to take the derivative of each term. The derivative of (remember the sho ...

Now, use the Power Rule to take the derivative of each term. The derivative of x = x . The derivati ...

Here we will find the derivative using the Chain Rule. We will also need the Quotient Rule to t ...

derivative. We get f(x) = = . Now we can take the derivative of each term. We get f′(x) = 3x^ ...

We find the derivative using the Quotient Rule, which says that if f(x) = , then f′(x) ...

We find the derivative using the Product Rule, which says that if f(x) = uv, then f′(x) = u + ...

. Here = and = 3x^2 . Now we plug x = 1 into the derivative. Note that where x = 1, ...

SOLUTIONS TO PRACTICE PROBLEM SET 6 2sin x cos x or sin 2x Recall that = (sin x) = cosx. Here ...

(2 csc x^2 )(−csc x^2 cot x^2 )(2x) = −4x csc^2 (x^2 )cot(x^2 ). 16 sin 2x Recall that (sin x) = cos x ...

11. Recall that (tan x) = sec^2 x and that (sec x) = sec x tan x. Using the Quotient Rule, we get ...

= 0. Next, because = 1, we can eliminate that term and we can distribute the −16 to get 2x − 16x − ...

5. −1 We take the derivative of each term with respect to x: + + = 0. Next, because = ...

isolate . Now, we take the derivative again: = . Next, because = 1 and , we get = . ...

because: = x^2 : = . Next, simplify the top and bottom: . Now, if we take the limit ...