# Is #e^x# the unique function of which derivative is itself? Can you prove it?

##
Is #e^x# the uniq function of which derivative is itself? Can you prove it? #f'(x)=f(x)=>f(x)=e^x# , is this true everytime? Is there any second function like this?

Is

Almost. If

Uniqueness of

Then:

and:

So equating the coefficients, we find:

So:

and:

Hence:

So:

Footnote

For example:

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the domain of #f(x)=sqrt(x+1)#?
- How do I find the stretches of a transformed function?
- How do you find the vertical, horizontal or slant asymptotes for #(e^x)/(7+e^x)#?
- How do you find the asymptotes for #F(x) = (-2x^2 + 1)/(2x^3 + 4x^2)#?
- How do you find the inverse of #y = 2x^2 - 3x +1# and is it a function?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7