If `f(x)=2x^(6)+3x^(4)+4x^(2)` , then f'(x) is

Options

A. an even function
B. an odd function
C. neither even nor odd
D. none of the above

Answer

To find the derivative of the function \( f(x) = 2x^6 + 3x^4 + 4x^2 \), we will follow these steps:

### Step 1: Identify the function
We have the function:
\[ f(x) = 2x^6 + 3x^4 + 4x^2 \]

### Step 2: Differentiate the function
To find \( f'(x) \), we will differentiate each term of the function with respect to \( x \).

Using the power rule of differentiation, which states that \( \frac{d}{dx}(x^n) = nx^{n-1} \), we will differentiate each term:

1. For the first term \( 2x^6 \):
\[ \frac{d}{dx}(2x^6) = 2 \cdot 6x^{6-1} = 12x^5 \]

2. For the second term \( 3x^4 \):
\[ \frac{d}{dx}(3x^4) = 3 \cdot 4x^{4-1} = 12x^3 \]

3. For the third term \( 4x^2 \):
\[ \frac{d}{dx}(4x^2) = 4 \cdot 2x^{2-1} = 8x \]

### Step 3: Combine the derivatives
Now, we combine the results from each differentiation:
\[ f'(x) = 12x^5 + 12x^3 + 8x \]

### Final Result
Thus, the derivative of the function \( f(x) \) is:
\[ f'(x) = 12x^5 + 12x^3 + 8x \]

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