y-x-2-1-At-Q-y-y-x-x-2-y-y-x-2-2x-x-x-2-2-Subtracting-1-from-2-y-y-x-2-2x-x-x-2-y-x-2-y-2x-x-x-2-Divide-through-by-

Question Number 127731 by Tosin Okunowo last updated on 01/Jan/21

y = x^{2} \dots \dots . . [1]

At Q, y + δ y = {(x + δ x)}^{2}

y + δ y = x^{2} + 2 x . δ x + {(δ x)}^{2} \dots . . [2]

Subtracting [1] from [2]

y + δ y = x^{2} + 2 x . δ x + {(δ x)}^{2}

y = x^{2}

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δ y = 2 x . δ x + {(δ x)}^{2}

Divide through by δ x

\frac{δ y}{δ x} = 2 x + δ x

If δ x \to 0, \frac{δ y}{δ x} \to \frac{dy}{dx} and ∴ \frac{dy}{dx} = 2 x

∴ If y = x^{2}, \frac{dy}{dx} = 2 x .