To find the derivative of the function \( y = 2x^3 + 5x^2 - 3x \), we will apply the power rule for differentiation. The power rule states that if \( y = ax^n \), then \( \frac{dy}{dx} = nax^{n-1} \).
Let's differentiate each term in the function:
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For the first term \( 2x^3 \): \[ \frac{d}{dx}(2x^3) = 3 \cdot 2x^{3-1} = 6x^2 \]
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For the second term \( 5x^2 \): \[ \frac{d}{dx}(5x^2) = 2 \cdot 5x^{2-1} = 10x \]
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For the third term \( -3x \): \[ \frac{d}{dx}(-3x) = -3 \]
Now, we can combine these results to find the derivative \( \frac{dy}{dx} \): \[ \frac{dy}{dx} = 6x^2 + 10x - 3 \]
Therefore, the derivative of the function is: \[ \frac{dy}{dx} = 6x^2 + 10x - 3 \]