## Calculus Tutorial

#### Intro

Derivatives are the foundation of calculus 1. Calculus 1 focuses on the study of derivatives and how it can change. There are different rules such as product, and quotient rules. These problems occur frequently and require such use of derivation techniques.

#### Sample Problem

Assume you have a fraction with only 1 dependent variable we will call t.

Find the value of f'(t) if f(t) = (3t^2)/(5t) when t = 1

#### Solution

1. requires quotient rule
2. (bottom fraction times derivative of top) – (top fraction times derivative of bottom) all over the bottom squared.
3. f'(t) = ((5t)(6t)-(3t^2)(5))/(25t^2)
4. when t = 1, f'(1)= (30-15)/25 = .6 which is the slope or m of the function.

More elaboration will occur when one on one with the student such as rules and theory explanation but for simplicity we will just handle it as is.

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