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Find the derivative of f(x) = 3x² + 2x - 5
math_question.jpg

Need help with this calculus problem!

I'll help you solve this step by step:

Answer: f'(x) = 6x + 2
Step 1: Apply the power rule to each term
Step 2: The derivative of 3x² is 6x (bring down the exponent and reduce by 1)
Step 3: The derivative of 2x is 2 (constant times x)
Step 4: The derivative of -5 is 0 (constants disappear)

Can you explain why the constant disappears?

Great question! Here's why:

Constants have a derivative of 0 because they don't change. The derivative measures rate of change, and since -5 is always -5 no matter what x is, its rate of change is zero.
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