# Math Help - Derivatives Of inverse functions; Derivatives and integrals involving exponential fun

1. ## Derivatives Of inverse functions; Derivatives and integrals involving exponential fun

Show that
a) Y= x exp-x statisfies the equation xy'=(1-x)y

2. Use product rule to get: $y = xe^{-x} \ \ \Rightarrow \ \ y' = e^{-x} - xe^{-x}$

So: $\text{LHS} = xy' = x \left(e^{-x} - xe^{-x}\right) = \cdots$

And: $\text{RHS} = (1-x)y = (1-x)(xe^{-x}) = \cdots$

Are they equal? If so, you're done.

3. do I have to use ln?

or what is the next step

4. What do you mean? We just want to show $xy' = (1-x)y$.

We've got an expression for $xy'$ and one for $(1-x)y$. Show that they're equal by simplifying and you're done.

5. oh I see thanks, I thinking something else?