10.4 Differentiating exponential functions

10.4.1 The derivative of exp⁡(x)\exp(x)

We can differentiate exe^{x} (or exp⁡(x)\exp(x)) from first principles using the definition of the limit. I am pretty sure this is not on many A Level mathematics specifications.

dd⁢x⁢[ex]\displaystyle\frac{d}{dx}\left[e^{x}\right] =limh→0ex+h−exh\displaystyle=\lim_{h\to 0}\frac{e^{x+h}-e^{x}}{h} (10.26)

TODO: finish writing this section up