If `y=4^(x)`, then `(dy)/(dx) = 4^(x)`

Answer

To solve the problem, we need to differentiate the function \( y = 4^x \) with respect to \( x \).

### Step-by-Step Solution:

1. **Identify the function**: We have the function given as \( y = 4^x \).

2. **Apply the differentiation rule for exponential functions**: The differentiation of \( a^x \) (where \( a \) is a constant) is given by the formula:
\[ \frac{dy}{dx} = a^x \cdot \log(a) \]
In our case, \( a = 4 \).

3. **Differentiate \( y = 4^x \)**:
Using the formula, we differentiate:
\[ \frac{dy}{dx} = 4^x \cdot \log(4) \]

4. **Conclusion**: The statement that \( \frac{dy}{dx} = 4^x \) is false. The correct derivative is:
\[ \frac{dy}{dx} = 4^x \cdot \log(4) \]

### Final Answer:
\[ \frac{dy}{dx} = 4^x \cdot \log(4) \]