**Differentiation** - used to find the **rate of change** of a function (the **gradient**). For a function *f(x) = a**xⁿ**, f'(x) = na**xⁿ⁻¹*. For example, the function *y *= 3*x*²+ 24*x *+ 10 differentiates into *dy/dx =* 6*x +* 24. The rule is: **Multiply** the **coefficient** by the **exponent**, then **decrease** the **exponent by 1**.

**Integration** - used to find the **area under a curve**. **By integrating** a **differentiated** function, you **return** to the **original function**. Therefore, the method of integration is quite logically following. **Increase** the **exponent by 1**, then **divide by** the **new exponent.**

∫*f'(x) dx = f(x) + C*

** where C is the constant of integration. It cannot be determined unless we know one coordinate through which f(x) passes.**

*This is called the fundamental theorem of calculus*

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