Question 3: Derivatives
Calculus
Level
2
f'''''''''''''...(x)=f'(x)
Find the set of non constant f(x) that fulfills this differential equation.
When a constant C appears twice in an answer, they represent different constants C.
ln(x)+C
sin(x)+C
e^Cx+C
e^x+C
Ce^x+C
1/x+C
C
cos(x)+C
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1 solution
d x n d n e x = e x for all n . Multiplying it by a constant C or adding a constant C to e x doesn't change this because of the linearity of the derivative, so C e x + C works.