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: Identify the function
The given function is:
\[ y = x^4 + 12x \]

### Step 2: Apply the differentiation rules
We will use the power rule of differentiation, which states that if \( y = x^n \), then:
\[ \frac{dy}{dx} = n \cdot x^{n-1} \]
We will apply this rule to each term in the function.

### Step 3: Differentiate each term
1. Differentiate \( x^4 \):
- Using the power rule:
\[ \frac{d}{dx}(x^4) = 4 \cdot x^{4-1} = 4x^3 \]

2. Differentiate \( 12x \):
- This is a linear term, and the derivative of \( ax \) (where \( a \) is a constant) is simply \( a \):
\[ \frac{d}{dx}(12x) = 12 \]

### Step 4: Combine the results
Now, combine the derivatives of both terms:
\[ \frac{dy}{dx} = 4x^3 + 12 \]

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

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