a) For the function y= e^-3x, determine dy/dx, d^2/dx^2 and d^3y/dx^3.

b) From the pattern in part a, state the value for �((d^n)y)/(d(x^n)).

2 answers

a)

dy/dx = (-3) * (e^-3x)

d^2/dx^2 = (-3) * (-3) * (e^-3x)

d^3y/dx^3 = (-3) * (-3) * (-3) * (e^-3x)

b)

Do you see a pattern above? What do you think the answer for this part should be based on that pattern?
Thank you very much! I appreciate the brisk response!