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

Step 1: Recall the Power Rule and Sum/Difference Rule

To find the derivative of a polynomial function, we use several basic differentiation rules. The power rule states that the derivative of $x^n$ is $nx^{n-1}$. The constant multiple rule allows us to pull constants out of the derivative, and the sum/difference rule lets us differentiate each term separately. The derivative of a constant is always zero.

Step 2: Apply the rules to each term

We apply the sum and difference rules to break down the derivative of the entire function into the derivatives of its individual terms. This allows us to handle each part of the polynomial separately.

Step 3: Differentiate each term

Now, we differentiate each term using the power rule and the constant multiple rule. For $x^3$, the derivative is $3x^2$. For $3x^2$, it's $3 \cdot 2x = 6x$. For $2x$, it's $2 \cdot 1 = 2$. And for the constant term $-5$, its derivative is $0$.

Step 4: Combine the derivatives

Finally, we combine the derivatives of all the individual terms to get the derivative of the original function $f(x)$. This gives us the final expression for $f'(x)$.

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