If y=e^(kx) , (d^(5)y)/(dx^(5)) = ?

Question

I know I'm supposed to take the fifth derivative but the dx^5 is confusing me...could someone please explain this and answer it?

Answer 1

Given function y = e^kx

Apply derivative on each side with respect of x.

By the chain rule d/dx(e^kx) = k(e^kx)

y' = ke^kx

Agian derivative on each side.

By the chn rule d/dx(e^kx) = k(e^kx)

y'' = k^2e^kx

y''' = k^3e^kx

y'''' = k^4e^kx

y''''' = k^5e^kx

d^5y/dx^5 = k^5e^kx