The derivative of \( y=3 x^{2}+ \) \( 2 x-5 \) is:

To find the derivative of the function \( y=3 x^{2}+ 2 x-5 \), we apply the power rule. The derivative of \( 3 x^{2} \) is \( 6 x \), the derivative of \( 2 x \) is \( 2 \), and the derivative of the constant \(-5\) is \( 0 \). So, the final derivative is \( y' = 6x + 2 \). Derivatives are not just an academic exercise; they're key to understanding motion, optimization problems, and even personal finance! For instance, they can help determine how fast a car accelerates or how to maximize profit in a business setup. Knowing the rate at which one quantity changes with respect to another shapes strategies and decisions in everyday life. If you're eager to dive deeper into derivatives, consider exploring resources like "Calculus Made Easy" by Silvanus P. Thompson. This book simplifies the concepts of calculus with engaging examples and practical applications. You might also find online platforms like Khan Academy handy, offering a plethora of videos and exercises to sharpen your derivative skills while having a little fun with math!