Question

3rd derivative of y=a/2(e^(x/a)+e^(-x/a)) (steps please)

Answer 1

Do you know what hyperbolic cosine and sine are?

Answer 2

i have the 2nd derivative worked out already y'' = a/(2a^2 ) ( e〗^(x/a) + e^(-x/a) )

Answer 3

needs to be worked out through differentiation

Answer 4

If you can get the second derivative, what's stopping you from getting the third?

Answer 5

need to investigate (d^(n)y)/(dx^(n)) for all positive odd integers for n

Answer 6

Well, a useful identity to know is \[\cosh(t)=\frac{e^{t}+e^{-t}}{2}\]\[\sinh(t)=\frac{e^{t}-e^{-t}}{2}\]

it's pretty straightforward to see that they are each their own derivatives, and what you have is essentially just the chain rule.

For example, \[\frac{d^n}{dx^n}(Ae^{b\ x})=Ab^n e^{b\ x} \] should make some sense.

Answer 7

thanks