Z=x/y, x=e^t, y=Lnt. Найти dz/dt.

Question

Z=x/y, x=e^t, y=Lnt. Найти dz/dt.

Answer 1

Z = e^t / ln(t)
dz/dt = (e^t)' / ln(t) + e^t * (1/ ln(t))' = e^t / ln(t) + e^t * (-1/ ln^2 (t)) * (1/t) = e^t / ln(t) - e^t/(t* ln^2 (t)) = ( e^t / ln(t) ) * ( 1 - 1/(t * ln(t)) )