Derivatives of Transcendental Functions - Theory & Concepts - Exponential Growth

Expand your differentiation skills to trigonometric, exponential, logarithmic, and hyperbolic functions, including inverse hyperbolic derivatives.

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Exponential Growth: $P(t) = P_0 e^{rt}$

Initial Population (

P_0

): 100

Growth Rate (

r

): 0.05

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Observation: The solid blue line represents the population $P(t)$ , and the dashed red line is its derivative $P'(t)$ . Notice how $P'(t)$ is always a constant multiple of $P(t)$ .

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Exponential Growth: P(t)=P0ertP(t) = P_0 e^{rt}P(t)=P0​ert

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Exponential Growth: $P(t) = P_0 e^{rt}$