The Determination of the Derivative using First Principles

1. Given f(x) = 1, determine f '(x). The tooltip gives an analytic definition of a constant function.
2. dy
   Given y = x  determine — by first principles
   dx
3. Determine  Dₓ[ x³ ] by first principles.
4. Given y = x⁻¹  determine
   dy
   — by first principles
   dx
5. Write the following expressions in exponential form