9. Find the derivative f(x) = v** (2x) -1° b. 1 - + (x+1)3(4x2)(2x2-1) a. *1-*+...
(2x - 1 if x < -1 2. Suppose f(x) = 2x2 - 4 if-1<x52 (log: (x - 1) if x > 2 a) Is f continuous at x = -1? Justify your answer completely. b) Is f continuous at x = 22 Justify your answer completely. 3. Suppose f(x) = x2 + 3x a) Using the definition of derivative, find f'(x). No credit will be given if shortcuts are used. b) Find the equation of the tangent line to...
2. Find the derivative of f(x) = 5(723 – 2x + 1)-3. 3. Differentiate f(x) = (3.2 + 10 – sin x)". O e 99+ ASUS VivoBook
12. Find the derivative of the following: y = ln(2x + 4x2 - 2x + 4)
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 + 3x – 5 at a = -2. [4 Marks] D1.2. (a) Find the derivative of y = 4 sin( V1 + Vx). (b) If y = sin(cos(tan(x2 + 3x – 2))), then find the first derivative. [3 Marks] D1.3. Using logarithmic differentiation, find the derivative of y = (sec x)+”.
1. Find Derivative: y=2x^3 ln(2x^3+7) a. y' = 36x^4 ÷ 2x^3+7 b. y'=12x^5 ÷ 2x^3+7 - 6x^2 ln (2x^3+7) c. y' = -36x^4 ÷ 2x^3 +7 d. y'=12x^5 ÷ 2x^3+7 + 6x^2 ln (2x^3+7) e. y'=2x^3 ÷ 2x^3+7 - 6x^2 ln (2x^3+7) f. 2x^3 ÷ 2x^3+7 + 6x^2 ln (2x^3+7) 2. Find exact value of the expression. Sin(arctan(x/4)) a. √16-x^2 ÷ x. b. x ÷√16-x^2. c. undefined. d. √16+x^2 ÷ x. e. 4 ÷ √16-x^2 f.none
Find the derivative of the function. y=5 e 2x2-3 dy 80 e 2x2x2 * + 20 e 2x2 X X Try again. Differentiate the exponential using the Chain Rule. to le 9(x) = g(x)g'(x) OK Find the derivative of the given function. y = (3x2 + 5x) -7x e -7x -7x y' = -21 e -7xx2 -29 +5e (Type an exact answer.) x X That's incorrect. The product rule states that if f(x) = u(x)•v(x), and if both u'(x) and...
The directional derivative of a function f(x, y, z) = 2x²yz - 100 at the point Po(1,-1,-1) in the direction of a vector v = 2i + 2j + k is Select one: 2 A. 3 B. 2 C. D.O. E. None of these answers
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
cewise Functions e function, evaluate lim f(x). 2 1-2x²+x+3 f(x) = { 2x2 – 3x + 3 (-3x - 2 if if xs1 1<x< 6 if x26 below:
11.1 Use the four step process to find the derivative of f(x) = -4r? - 2x +3. (a) Find f(x+h) (b) Find f(x+h)-f(x) (c) Find $(2+ h) – f(x) (d) Find lim f(x+h)-f(2) h-10 11.2 Use the rules to find the derivatives of the following functions. (a) f(x) = 212 (b) f(x) = .24x1/2 (c) f(x) = 134. (d) f(x) = 420-1 (e) f(x) = -.02.2 + 45x - 200.