Derivative of exponential functions

[Riles246]

Homework Statement

d/dT (e^-E₀/(kT))

Homework Equations

d/dx(e^x) = e^x

The Attempt at a Solution

e^-E₀/(kT) * E₀/kT² ?

Do you use the chain rule on the exponent of e?

 

[Hootenanny]

Homework Statement

d/dT (e^-E₀/(kT))

Homework Equations

d/dx(e^x) = e^x

The Attempt at a Solution

e^-E₀/(kT) * E₀/kT² ?

Do you use the chain rule on the exponent of e?

Looks spot on to me . And yes, you would use the chain rule (followed by the power rule on the exponent) to differentiate the function.

 

[alphachapmtl]

if u=u(x),
d/dx (e^u) = e^u du/dx
d/dx (e^(1/x)) = e^(1/x) (-1)/(x^2)
d/dx (e^(a/x)) = e^(a/x) (-a)/(x^2)
d/dx (e^(a/bx)) = e^(a/bx) (-a/b)/(x^2)