Activity 1.4.3.
For each of the listed functions, determine a formula for the derivative function. For the first two, determine the formula for the derivative by thinking about the nature of the given function and its slope at various points; do not use the limit definition. For the latter four, use the limit definition. Pay careful attention to the function names and independent variables. It is important to be comfortable with using letters other than \(f\) and \(x\text{.}\) For example, given a function \(p(z)\text{,}\) we call its derivative \(p'(z)\text{.}\)
(a)
\(f(x) = 1\)
(b)
\(g(t) = t\)
(c)
\(p(z) = z^2\)
(d)
\(q(s) = s^3\)
(e)
\(F(t) = \dfrac{1}{t}\)
(f)
\(G(y) = \sqrt{y}\)
