# Applying rules of differentiation

### Rules for Differentiation

There are a number of differentiation rules that you need to be familiar with.

For example, find the derivative of:

- \( y = \frac{x^\frac{3}{2}}{4} - 3\sqrt{x} + 8\,\) using the basic rules.
- \({\displaystyle 5x - x^2 + 3x^3 + 2 \ln x\,}\) using the basic rules.
- \(y = \cos^2\theta\) using the chain rule.
- \( y = (3 + x^2)(2 + \ln x) \) using the product rules.
- \( \displaystyle y = \frac{x^2}{\sqrt{x-1}} \) using the quotient rule.