Find the derivative of the following functions:

Question

a) f(x)=(3x^2-6 )/(x+2)

b) g(x)=sin(e^2 +5x)

c) j(x)=6xe^x

d) Your velocity is v(t)= t^2 = 1 for 0≤ t ≤ 4. Find or estimate the distance traveled during this time.

Answer 1

F'(x) = 3(x^2 +4x +2/(x+2)^2
F'(x) = 5cos(5x + e^2)
F'(x) = 6x(e^x) + e^x (6)
= 6e^x (x +1)

Answer 2

a. F'(x) = 3(x^2 +4x +2/(x+2)^2
b. F'(x) = 5cos(5x + e^2)
c. F'(x) = 6x(e^x) + e^x (6)
= 6e^x (x +1)

Answer 3

Thank you very much!