Differentiation of Logarithmic Functions

1. f(t) = ln [ ln (5t +2) ]
f'(t) = d f(t) /d (ln(5t+2) * d(ln(5t+2) / d(5t+2) * d(5t+2) /dt
= [1 / ln(5t+2)] [1/(5t+2)] (5)
= 5 / [(5t+2) ln(5t+2)]

2. F(w) = ln(3 - 4w) / e^(2w)
F'(w) = {e^(2w) [1/(3-4w)] (-4) - ln(3-4w) (2)(e^2w)} /e^(4w)
= [2(4w-3) ln(3-4w) - 4] / [(3-4w) e^(2w)]

1
f'(t)={ 1/[ ln (5t + 2)] } [1/(5t + 2)] x 5
=5/ [(5t + 2)ln (5t + 2)]

2
F'(w)={ e^(2w)[1/(3-4w)]x(-4) - ln(3-4w) x e^(2w) x2 }/ e^(4w)
= -2[ 2/(3-4w) + ln(3-4w)]/e^(2w)