Question

what is the derivative of (1+h)^ln(1+h)

Answer 1

let y=(1+h)^(ln(1+h))
lny=ln(1+h)^(ln(1+h))
lny=ln(1+h)*ln(1+h)
lny=[ln(1+h)]^2
take derivative of both sides
y'/y=2ln(1+h)*1/(1+h)

Answer 2

so y'={2yln(1+h)}/(1+h)
y'=[(1+h)^(ln(1+h))*ln(1+h)]/(1+h)

Answer 3

times 2