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

Ask by Bright Sullivan. in Sierra Leone
Mar 11,2025

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The derivative of \( y = 3x^2 + 2x - 5 \) is \( y' = 6x + 2 \).

Solución

1. Start with the function: \[ y = 3x^2 + 2x - 5 \] 2. Find the derivative term by term. - For \(3x^2\), use the power rule \( \frac{d}{dx}x^n = nx^{n-1} \): \[ \frac{d}{dx}(3x^2) = 3 \cdot 2x^{2-1} = 6x \] - For \(2x\), the derivative is: \[ \frac{d}{dx}(2x) = 2 \] - For the constant \(-5\), the derivative is: \[ \frac{d}{dx}(-5) = 0 \] 3. Combine the derivatives: \[ y' = 6x + 2 \]

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Mind Expander

To find the derivative of the function \( y = 3x^2 + 2x - 5 \), we apply the power rule. The derivative of \( 3x^2 \) is \( 6x \), the derivative of \( 2x \) is \( 2 \), and the derivative of a constant (like \(-5\)) is \( 0 \). Therefore, the derivative \( \frac{dy}{dx} = 6x + 2 \). If you're ever unsure about applying rules of differentiation, just remember that practice makes perfect! Work on a variety of polynomial functions, and soon, finding derivatives will feel second nature. A common mistake is forgetting that constants disappear when derived; always double-check yourself! Additionally, if you're interested in expanding your knowledge further, textbooks like "Calculus" by James Stewart offer thorough explanations and practice problems. Online resources such as Khan Academy also provide interactive exercises that can help solidify your understanding of derivatives in a fun and engaging way.

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