3. (6 points each) Differentiate the following functions. Do not simplify your answer. a. f(x) =...
2. (4pts each) Find the derivative of the following functions: You do not need to simplify the answer. CIRCLE FINAL ANSWER. a. f(x) = 2x2e-1 + 7e2x-1 + 3e2e cos (36) b. g(t) = 1+sin(3) c. h(x) = ln(x2). arctan(kx) (k E R) d. f(x) = sin(x) sin(x)
Prob.II. Differentiate the following functions, and simplify. 1. f(x) 2x-3 x+4 2. f(x) = x²(x - 2)* 3. f(x) = In (x V1 - x2) 4. f(x) = x2e-* 5. Find dy/dx = y' for the equation x2 + y2 = 25 and find y" (check H.W)
5. Differentiate the following functions by filling in the chart. Original Function Rewrite Differentiate Simplify a. f(x)= V.x2 b. f(x)= c. f(x)= 4 3.x2 T d. f(x)= (5x)2
evaluate the first limit
13] 3. Differentiate the following. Simplify your answers. a. f(x) = (x-2)2 (x + 3)" 131 r+1 b. f(x)s 131 x+1 Page 3 of 12
13] 3. Differentiate the following. Simplify your answers. a. f(x) = (x-2)2 (x + 3)" 131 r+1 b. f(x)s 131 x+1 Page 3 of 12
5. (5 points each) Compute the following derivatives. Do not simplify. dy (a) Let y = cos (3.1). Find der (b) Let f(t) = de-+ +5e". Find f(*)(t). (c) Let g(t) = ln(2) sec(1). Find d'(I). df (d) Let f(t) = " + x + ex. Find dar ind
1. Differentiate each of the following functions: (a) 22--6 (b) (1+) (c) In(x3 + x) (d) (2 – 2)e-2 (f) (In x)(:– 1)ez"
Consider the following functions. f(x)=1/x and g(x)= x^3 Find the formula for (f∘g)(x) and simplify your answer. Then find the domain for (f∘g)(x) . Round your answer to two decimal places, if necessary. Also, Find the formula for (g∘f)(x) and simplify your answer. Then find the domain for (g∘f)(x) . Round your answer to two decimal places, if ny.
#35,37
In Exercises 21 through 38, differentiate the given function and simplify your answer 21. f(x) (2x 3)14 22. fx) 23. f(x) = (2x + 1)4 24. f(x) = V 5x6-12 25. fx)-(a 4r3 78 26. ft) (3r 729)5 27, f(t) = V5 3x 28. f(x)=- (6x2 +5x+ 1)2 5rt_ V4x2 30. 4x +1 31. f(x)=: (1-x2)4 2 3(5x4 1)2 32. f(x) = (1-x2)4 (135) f(x) = (x + 2)3(2x-1)5 36. f(x) 2(3x 1)(5x 3)2 (1 -x 1 - 5x2...
(15 points) Find the derivative of the following functions. You do not have to simplify answers. ecos (22+2+1) 1. (5 points) f(x) = 2. (5 points) g(x) = So" con (+0+1)dt + So sin tdt 3. (5 points) h(x) = Licen (o? +++ 1)dt
1. Find and simplify the derivative of each of the following functions: In(2 1) 2x 1) tan 1In(tan) (a) (x)In (b) f(x) = (412-1)3 In(4z?-1) (g) f(r)-n (n) f(x) = ln(sec 3r-tan 3r) 1 +x ln a