I need to find the first 2 orders of the taylor series on the expression below.

sqrt(Psi_s0 + Phi_t*exp((Psi_s0-2*Phi_F - V_SB)/Phi_t))

where Phi_t*exp((Psi_s0-2*Phi_F - V_SB)/Phi_t) is defined as Xi, and the taylor series is around Xi = 0.

Printable View

- Jun 15th 2008, 08:23 PMwas1984Taylor Expansion on d/d(f(x))[sqrt(x+f(x))]
I need to find the first 2 orders of the taylor series on the expression below.

sqrt(Psi_s0 + Phi_t*exp((Psi_s0-2*Phi_F - V_SB)/Phi_t))

where Phi_t*exp((Psi_s0-2*Phi_F - V_SB)/Phi_t) is defined as Xi, and the taylor series is around Xi = 0. - Jun 15th 2008, 08:56 PMMathstud28
- Jun 15th 2008, 08:57 PMwas1984
Yes, thank you, that is correct.

- Jun 15th 2008, 09:00 PMMathstud28
- Jun 15th 2008, 09:03 PMwas1984
The variable we are differentiating with respect to is Xi, which is the second term under the square root.

- Jun 15th 2008, 09:11 PMwas1984
I'll try to elaborate. We are setting

Then we are solving the series around

So I actually want expand an equation of the form for , and I only need the first two terms, fortunately. :)