Question

数学求In（dy／dx）的值Y＝e＾t+1x＝e^t求In（dy／dx）的值

Answer 1

I agree with 数学乞佬.

Here is what you can do step by step:

Since x = e^t,so t = ln x

Y = e^(t+1) = e^(ln x +1)

let ln x + 1 = u

dy/dx = d[e^(t+1)]/dx = d[e^(ln x +1)]/dx = d(e^u)/dx = (e^u) * du/dx

=e^(ln x +1) * d(ln x +1)/dx = e^(ln x +1) * (1/x)

Since x = e^t

dy/dx = e^[ln(e^t) +1] * (1/e^t) = e^(t+1) * (1/e^t) = e^(t+1)/e^t

=e

Therefore,

ln (dy/dx) = ln e = 1