Evaluate differentiation of y with respect to x :
`y=x^(4)+12x`

Explanation

To evaluate the differentiation of \( y \) with respect to \( x \) for the function \( y = x^4 + 12x \), we will follow these steps:

### Step 1: Write down the function
We start with the given function:
\[ y = x^4 + 12x \]

### Step 2: Apply the differentiation operator
We need to find the derivative \( \frac{dy}{dx} \). This can be expressed as:
\[ \frac{dy}{dx} = \frac{d}{dx}(x^4 + 12x) \]

### Step 3: Differentiate each term separately
Using the property of derivatives that states the derivative of a sum is the sum of the derivatives, we can differentiate each term:
\[ \frac{dy}{dx} = \frac{d}{dx}(x^4) + \frac{d}{dx}(12x) \]

### Step 4: Differentiate \( x^4 \)
Using the power rule of differentiation, which states that \( \frac{d}{dx}(x^n) = n \cdot x^{n-1} \):
\[ \frac{d}{dx}(x^4) = 4x^{4-1} = 4x^3 \]

### Step 5: Differentiate \( 12x \)
Since \( 12 \) is a constant, we can factor it out:
\[ \frac{d}{dx}(12x) = 12 \cdot \frac{d}{dx}(x) = 12 \cdot 1 = 12 \]

### Step 6: Combine the results
Now, we combine the results from the differentiation of each term:
\[ \frac{dy}{dx} = 4x^3 + 12 \]

### Final Result
Thus, the derivative of \( y \) with respect to \( x \) is:
\[ \frac{dy}{dx} = 4x^3 + 12 \]

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