## Calculus Tutorial

*Different Differentiation Rules*

#### Intro

Any problem that can be solved with the quotient rule can also be solved with the product rule and chain rule.

#### Sample Problem

Find the first derivative of:

#### Solution

Quotient rule:

Separate the numerator and denominator into two separate functions, then find their derivatives.

Plug into the quotient rule formula:

You can expand the answer if you like, but this is sufficient.

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Now for the Product Rule. This time, we will turn the denominator into a negative exponent:

g(x) will remain the same, but h(x) and h'(x) will look like this using the chain rule:

And plug into the product rule:

You should arrive at the same answer in both cases

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