21. Find the derivative of each of the following functions by applying the product rule a....
10. Use the limit definition of the derivative to calculate the derivatives of the following functions. a. f(x) = 2x2 – 3x + 4 b. g(x) = = x2 +1 1 x2 +1 c. h(x) = 3x - 2 a. 11. Find the derivative with respect to x. x² - 4x f(x)= b. y = sec v c. 5x2 – 2xy + 7y2 = 0 1+cos x 1-cosx cos(Inu) e. S(x) = du 1+1 + + f. y =sin(x+y) g....
4. Find the following limits. 473 + 5x² - 2x+2) 273 - 2x + 100 203 - +3 (b) limz+03,3 - 2x2 – 3x + 2 (a) limz+ f (x +h)-f(x) 5. Find the derivative using the definition /' () = lim-0- (a) f(x) = 22 - 2 (b) f(x) = 2x + 3 6. Find the derivative using the formula including product rule and quotient rule (Don't use the definition in # 5) 3.- 2 (a) f(x) = 33...
Problem ll C10 points) choose any 2 problems In Problems 21-32, find the derivative of each function at the given number. 21. f(x) = -4x + 5 at 3 22. f(x) = -4 + 3x at 1 24. f(x) = 2x² +1 at -1 25. f(x) = 2x² + 3x at 1 23. f(x) = x2 - 3 at 0 26. f(x) = 3r? - 4x at 2
2. (each 1 mark) Find the derivative of the following functions: 9x + 7 (a) y = 92 - 1 (b)r = (02 9016 /09 - 9 ( 9 ) (c) y=rºcot x + 9x2 cos x – 14x sin x 9t sint (d) s = cost + +9 (e) h(x) = cº sin (vą) + 240 sec (1) ) 10 (f) f(0) = (_sin 98 (1+cos 90 ) (g) g(x) = (1 + csc(+10) + In (922 – 8)...
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)
Find the derivative of the following functions: Inx 22 C. a. F(x) = In (3x) b. Y=: Y=52x-1 d. Y= log1032 e. Y=In(x2-2)2/3 f. Y= In g. Y= log2 (2x - 1) h. Y= 8** e 1+e+
Find the derivatives of the following functions (A) y=xt-x2 (B) y=x2 (C) y-3x3 + 4x -3 (D) y=x (F) f(x)- 100x100 (G) fx)- (H) f(x)=- 1-5r ) f(x)= (J f(x) - (x + 1)(x3 +5x + 2) (Requires quotient rule) 4+x For f(x) = 6x3, find f(x) and f"(x), and fm(x). For f(x)- 5x3 -3x2+x-20, find f(x), f"(x), and f""(x)
Signature: 19.( 9 marks) Find the derivative of the following functions. 1. V = 1 " b. y = sinsx - Cos 3x c. y = (sec 5x + tan-'(1 - x)) 20. (6 marks) Find the derivative of the following functions. a) y = ln(1 - 3x) + 4* b) y = -2x + 3x +1
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
5. Use the limit definition to find the derivative of f(x) = V3x + 2. (6 points) 6. Find the derivatives of the following functions. Do not simplify after taking the derivative. 5 points each a. f(x) = (4x2 +1) c. h(x) = arcsin(3x2+ 2x-1) b. h(x) = 3sec(x2)