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If y=f(x) then dy/dx

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If y=f(x) then dy/dx

Posted by Azhar Rana 6 years, 4 months ago

CBSE > Class 12 > Mathematics

1 answers

Subham Agarwal 6 years, 4 months ago

y=f(x) y = f(x) 1. Add Δx When x increases by Δx, then y increases by Δy : y + Δy = f(x + Δx) 2. Subtract the Two Formulas From: y + Δy = f(x + Δx) Subtract: y = f(x) To Get: y + Δy − y = f(x + Δx) − f(x) Simplify: Δy = f(x + Δx) − f(x) 3. Rate of Change To work out how fast (called the rate of change) we divide by Δx: ΔyΔx = f(x + Δx) − f(x)Δx 4. Reduce Δx close to 0 We can't let Δx become 0 (because that would be dividing by 0), but we can make it head towards zero and call it "dx": Δx right arrow dx You can also think of "dx" as being infinitesimal, or infinitely small. Likewise Δy becomes very small and we call it "dy", to give us: dydx = f(x + dx) − f(x) ÷ dx

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