To differentiate the function $f(x) = 2x^2 + 3x - 5$, we can apply basic differentiation rules. Here are the steps:

1. Identify the function components: The function $f(x)$ consists of three terms:

   • $2x^2$
   • $3x$
   • $-5$

2. Differentiate each term separately:

   • For the term $2x^2$: Use the power rule, which states that $\frac{d}{dx}(x^n) = nx^{n-1}$. $\frac{d}{dx}(2x^2) = 2 \cdot 2x^{2-1} = 4x$
   • For the term $3x$: Use the power rule, where $x$ is $x^1$. $\frac{d}{dx}(3x) = 3 \cdot 1x^{1-1} = 3$
   • For the constant term $-5$: The derivative of a constant is zero. $\frac{d}{dx}(-5) = 0$

3. Combine the differentiated terms: Add the derivatives of each term to get the derivative of the entire function. $f'(x) = 4x + 3$

So, the derivative of $f(x) = 2x^2 + 3x - 5$ is $f'(x) = 4x + 3$.

Would you like more details or have any questions?

Here are 8 related questions for further exploration:

1. How do you find the second derivative of $f(x) = 2x^2 + 3x - 5$?
2. What is the derivative of the function $g(x) = x^3 - 4x^2 + 7x - 10$?
3. How do you apply the chain rule to the function $h(x) = (3x^2 + 2x - 1)^5$?
4. What are the critical points of the function $f(x) = 2x^2 + 3x - 5$?
5. How can you use differentiation to find the local maxima and minima of a function?
6. What is the derivative of the exponential function $e^x$?
7. How do you differentiate the trigonometric function $\sin(x)$?
8. What are the applications of differentiation in real-world problems?

Tip: When differentiating polynomial functions, remember to apply the power rule term-by-term for accurate results.