Question:

Find the derivative of the function $f(x) = 3x^2 - 5x + 2$.

Answer:

To find the derivative of the function $f(x) = 3x^2 - 5x + 2$, we can use the power rule for differentiation, which states that if $f(x) = cx^n$, then $f'(x) = ncx^{n-1}$.

Step 1: Write down the function: $f(x) = 3x^2 - 5x + 2$.

Step 2: Apply the power rule for each term in the function.

For the term $3x^2$, the power rule gives us $3 \cdot 2x^{2-1} = 6x$.

For the term $-5x$, the power rule gives us $-5 \cdot 1x^{1-1} = -5$.

For the constant term $2$, the power rule gives us $0$, since any constant raised to the power of 0 is 1.

Step 3: Combine the derivatives of each term.

The derivative of $f(x)$ is $f'(x) = 6x - 5 + 0$.

Simplifying gives us $f'(x) = 6x - 5$.

Therefore, the derivative of the function $f(x) = 3x^2 - 5x + 2$ is $f'(x) = 6x - 5$.