What is the difference between deriving and deriving using first principles ?
for example how would you use first principles to find the derivative of y=7/(rootx + 6)
and y = 1 / 2x
Finding derivatives by first principles means to use the definition of the derivative. recall that we define the derivative of a function $\displaystyle f(x)$ as follows
$\displaystyle f'(x) = \lim_{h \to 0} \frac {f(x + h) - f(x)}h$
provided the limit exists.
now use that to find the derivatives. you can check your answers by doing the derivatives the short way