To find the derivative of the function \( f(x) = 3x^2 + 2x - 5 \), we can apply the power rule. The power rule states that if you have a term \( ax^n \), the derivative is \( nax^{n-1} \).
Now, let's differentiate each term:
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For \( 3x^2 \): \[ \frac{d}{dx}(3x^2) = 2 \cdot 3x^{2-1} = 6x \]
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For \( 2x \): \[ \frac{d}{dx}(2x) = 1 \cdot 2x^{1-1} = 2 \]
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The derivative of the constant \( -5 \) is \( 0 \).
Now, we combine the derivatives of all the terms: \[ f'(x) = 6x + 2 + 0 = 6x + 2 \]
So the derivative of \( 3x^2 + 2x - 5 \) is: \[ \boxed{6x + 2} \]