Find the derivative of`y = log 4x`

Answer

To find the derivative of the function \( y = \log(4x) \), we can follow these steps:

### Step 1: Rewrite the logarithmic expression
Using the property of logarithms that states \( \log(AB) = \log A + \log B \), we can rewrite the function:
\[ y = \log(4x) = \log(4) + \log(x) \]

### Step 2: Differentiate the expression
Now, we differentiate both sides with respect to \( x \):
\[ \frac{dy}{dx} = \frac{d}{dx}(\log(4)) + \frac{d}{dx}(\log(x)) \]

### Step 3: Evaluate the derivatives
The derivative of a constant (in this case, \( \log(4) \)) is 0. The derivative of \( \log(x) \) is \( \frac{1}{x} \):
\[ \frac{dy}{dx} = 0 + \frac{1}{x} \]

### Step 4: Write the final answer
Thus, the derivative of \( y = \log(4x) \) is:
\[ \frac{dy}{dx} = \frac{1}{x} \]