Derivatives and Chain Rule: Solving for x and y

[annoymage]

Homework Statement

let x=e^t and define y(x(t))=Y(t)

Show that x(d/dx)y=(d/dt)Y

Homework Equations

n/a

The Attempt at a Solution

i try using chain rule but

x(dy/dt)(dt/dx) and i don't know how to make it to be dY/dt, and i don't have clue what is the point of x=e^t.. help T_T

 

[HallsofIvy]

Look at it the other way around. If $x= e^t$ then $dy/dt= (dy/dx)(dx/dt)= e^t(dy/dx)= x(dy/dx)$. The point of "$x= e^t$ is that the derivative of $x= e^t$ is $x= e^t$.

 

[annoymage]

my goodness, thank you very very very much