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

Derivatives are one of the most important concepts in mathematics (calculus) which have many applications in various other fields. We can calculate the slope of any curve using derivatives.

## 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}.

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