# If f(x) = e^{x}, what is equal to f'(e)?

Derivatives are one of the most important concepts in calculus which have many applications in various other fields.

## Answer: If f(x) = e^{x}, then f'(e) = e^{e}.

Let's understand the solution in detail.

**Explanation:**

We use the first principle formula of derivatives to calculate the result.

Hence, by first principle of derivatives, we have:

f'(x) = lim_{h→0 }{ f(x + h) - f(x) } / h

Hence,

f'(e) = lim_{h→0 }{ f(e + h) - f(e) } / h

= lim_{h→0 }{ e^{e + h} - e^{e} } / h

= lim_{h→0 }[ e^{e} (e^{h} - 1) ] / h

Now, we know that lim_{h→0 }{ (e^{h} - 1) / h } = 1, We can also verify this by the L'Hopital's rule.

Hence, f'(e) = e^{e}.

Check out the online derivatives calculator.

### Hence, if f(x) = e^{x}, then f'(e) = e^{e}.

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