early and late transcendentals

in teaching calculus, there are two approaches: early transcendentals and late transcendentals.

in early transcendentals, logarithmic and exponential functions will be taught after the definition of derivative. the definition of $a^b$ is $\lim_{q \to b} a^q$ and there exists a number $e$ such that $\frac{d}{dx} e^x |_{x = 0} = 1$ and $\ln{x}$ is definied as the inverse function of $e^x$ .

in late transcendentals, the traditional approach, logarithmic and exponential funcitons will be taught after the introduction of integration. the definition of $\ln{x}$ is $\int_{1}^{x} \frac{1}{t} dt$ and $e^x$ is defined as the inverse function of $\ln{x}$

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