Question

hi, can anyone help me to understand how to find the derivatives of exponential functions?

Answer 1

the shortcut: if the function is of the form: a^x, then the derivative is (a^x)*ln(a)
So d/dx (2^x) = 2^x * ln2
why?
you can show that the limit process on the slope equation gives: lim(h->0) a^x (a^h - 1)/h with a really straight forward simplification
then lim(h->0) (a^h-1)/h = ln(a)