Calculus
Class 11-12

Derivative from First Principles

f(x)=limh0f(x+h)f(x)hf'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
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f'(x) = lim[h→0] (f(x+h) - f(x))/h

Adjust Variables

h (step size)
h =
0.0011

The fundamental definition of derivative as instantaneous rate of change. This limit is what makes calculus possible.

Real-World Applications

Speedometer reading — Instantaneous velocity is derivative of position.

Stock price changes — Rate of price change at any moment.

Population growth rate — Instantaneous growth at any time.

Chemical reactions — Reaction rate as derivative of concentration.

Physics — Acceleration as derivative of velocity.

Economics — Marginal cost as derivative of total cost.

Medicine — Rate of drug absorption in bloodstream.

Engineering — Stress rate in material deformation.

Climate — Rate of temperature change.

Finance — Sensitivity of option price to underlying (Delta).

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