question 1 solve the following using Derivative
(a) For each of the following functions, identify which rule (the product rule, quotient rule or chain rule) you would use to differentiate the function. Give a 1-2 sentence explanation justifying your answer.
(a) f(x) = cos(x)/ 2x2, x doesn't equal 0
(b) y = ln(x2 − 11x + 30)
(c) f(x) = e 5x sin(2x)
(d) Use the product rule to differentiate y = sin(2x) × (4x3− x).
(e) Use the quotient rule to differentiate y = sin(2x)/ e5x
(f) Use the chain rule to differentiate y = ln(x2 + 4)
(e) The displacement (in metres) of a particle at time t seconds is given by
s = 160000t2 − 400t4 for 0 ≤ t ≤ 20.
-Find the velocity of the particle v = ds/dt .
- Find the acceleration of the particle a = d2s/ dt2 .
-What is the displacement, velocity and acceleration at time t = 1 second?
