§2.1 Elementary derivative rules

Introduction

Some Key Notation

Constant, Power, and Exponential Functions

Use the limit definition of the derivative for $f(x) = x^2$: the difference quotient simplifies to $2x + h$ before the limit. Compute $f'(4)$.

Which of the following functions has derivative identically equal to zero?

Use the rule for power functions to differentiate $h(t) = t^{7/5}$. Which expression is $\frac{dh}{dt}$?

Let $g(z) = 7^z$. Which expression is $g'(z)$?

If $f(t) = \pi$, then $f'(t) = 0$ for every value of $t$.

For $h(w) = w^{3/4}$, compute $h'(1)$ as a fraction.

Let $s(q) = q^{-1}$. Which expression is $\frac{d}{dq}[s(q)]$?

For $m(t) = \frac{1}{t^3}$, compute the instantaneous rate of change $m'(1)$.