d(e^x) / dx = e^x {exponential function, differentiation}. d(e^u(x)) = e^u(x) * du(x). Limit of (1 + 1/n)^n is e. Limit of (1 + h)^(1/h) is e. Limit of (1 + dx)^(1/dx) is e. Limit of (1 + (x / dx))^(x / dx) is e. On semi-log graph paper, y = b * a^x makes straight lines. On log-log graph paper, y = b * x^a makes straight lines.
If x > 0, dln(x) = 1/x {logarithmic function, differentiation}. If u(x) > 0, dln(u(x)) = (1 / u(x)) * du(x). (v(x))^a = e^(a * ln(v(x))). (v(x))^z(x) = e^(z(x) * ln(v(x))).
3-Calculus-Differentiation-Function
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Date Modified: 2022.0225