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What is the differentiation of y = 2x2 − 4x using the power rule?

May 2, 2026Mathematics

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Answer

\frac{dy}{dx} = 4x - 4

Graph of y = 2x² − 4x

2 steps

Here is the differentiation for part c):

Differentiate each term using the power rule.
$y = 2x^2 - 4x$ $\frac{dy}{dx} = \frac{d}{dx}(2x^2) - \frac{d}{dx}(4x)$
Apply the power rule to each term.
$\frac{dy}{dx} = 2 \cdot 2x^{2-1} - 4 \cdot 1x^{1-1}$ $\frac{dy}{dx} = 4x - 4x^0$ $\frac{dy}{dx} = \boxed{4x - 4}$

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