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# 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:

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