`(d)/(dx)(e^(100))`=…………………

Options

A. `e^(100)`
B. 0
C. `100^(e^(99))`
D. None of these

Answer

To solve the problem \(\frac{d}{dx}(e^{100})\), we need to differentiate the given expression with respect to \(x\).

### Step-by-Step Solution:

1. **Identify the Expression to Differentiate:**
The expression given is \(e^{100}\).

2. **Recognize the Nature of the Expression:**
\(e^{100}\) is a constant because it does not contain the variable \(x\). The value \(e^{100}\) is a fixed number.

3. **Apply the Differentiation Rule for Constants:**
The derivative of a constant with respect to any variable is always zero. Mathematically, if \(C\) is a constant, then:
\[ \frac{d}{dx}(C) = 0 \]

4. **Differentiate the Given Expression:**
Since \(e^{100}\) is a constant, we apply the rule:
\[ \frac{d}{dx}(e^{100}) = 0 \]

### Final Answer:
\[ \frac{d}{dx}(e^{100}) = 0 \]