2. Find the derivative of each of the following functions: y = x12 (i) (ii) (iii) (iv) y = 3x-¹ y = (x²-3x) (4x + 6) y = (x²+3x) (x3-5)

Find the derivative of each function. 1. f(x) = 5x²(3x²–16) 3.y y--x*+78 +x2 %3D bo 98 150 X -X"f} | 3x+2 4.y= 2. y = 5x-3 35

Find the first derivatives of y = x³ – x + 2 e*

5. Find the first and second order derivatives of the function (a) f(x) = 0.001x5 -0.002x³ (b) G(r) = √r + ³√r.

1. Suppose the function V represents the number of people vaccinated for COVID-19 in Kalamazoo country. (a) What can you conclude about the first and second derivatives of V from the statement "The number of people vaccinated is increasing faster and faster"? For your conclusion, choose from among: positive, negative, zero, or other. If other, please explain. i. V'(t) is ii. V"(t) is (b) What can you conclude about the first and second derivatives of V from the statement "The number of people vaccinated is close to reaching an all time high"? For your conclusion, choose from among: positive, negative, zero, or other. If other, please explain. i. V'(t) is ii. V"(t) is

2. Find the anti-derivative of · ƒ (x) = 2x¹ − 5√x³ −3 −2ex + a. - 6 = 1 + ₁ x 1 1+x² b. f(x) = -3sin x - 2cosx + 6csc²x - 8 csc x cotx

1

12.3 and 12.4) K Find the derivative. f(x)= 5 (2x-3)* <-40 (2x-3)³ OA f(x)=- 5 8(2x-3)5 OB. f(x)=- OD. f'(x)= 5 4(2x-3)³ O c. f(x)=- -40 (2x-3)5 Que

- If e*y cosxz = 10 and z is an implicit function of x and y then find zx and zy by implicit differentiation.