Solve the derivative of `y=log 2x^3`

Answer

To solve the derivative of the function \( y = \log(2x^3) \), we can follow these steps:

### Step 1: Rewrite the function
We start with the function:
\[ y = \log(2x^3) \]

### Step 2: Use the properties of logarithms
Using the property of logarithms that states \( \log(ab) = \log a + \log b \), we can rewrite the function:
\[ y = \log(2) + \log(x^3) \]
Using another property of logarithms, \( \log(x^n) = n \log(x) \), we can simplify further:
\[ y = \log(2) + 3\log(x) \]

### Step 3: Differentiate the function
Now we differentiate \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = 0 + 3 \cdot \frac{1}{x} \]
This simplifies to:
\[ \frac{dy}{dx} = \frac{3}{x} \]

### Final Answer
Thus, the derivative of \( y = \log(2x^3) \) is:
\[ \frac{dy}{dx} = \frac{3}{x} \]

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