3.2 HW Problems

Table of Contents:

Calculating Derivatives from the Definition

• The process of calculating a derivative is called differentiation. We use the notation:

$$ \frac{d}{dx}f(x) $$

Derivative of the Reciprocal Function

$$ \frac{d}{dx}\biggr(\frac{1}{x}\biggr) = \, -\frac{1}{x^2}, \enspace x \neq0 $$

$$ \frac{d}{dx}\biggr(\frac{1}{x}\biggr) = \, -\frac{1}{x^2}. $$

Derivative of the Square Root Function

$$ \frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}, \enspace x>0 $$

Notation