**Definition** – **Differentiation** is the **rate of change of the function value, f(x)** to the **change in the value of ‘x’.**Finding a derivative of any function is the same thing as finding the slope at a particular point. Hence derivative is also called as the **slope of the tangent drawn** at any point on any curve!

**Example: **Given f(x) = 3x, find its derivative using the above formula.

So, dy/dx = [f(x+∆x) – f(x)] / ∆x

** -> **dy/dx= [3(x+∆x) – 3x] / ∆x

** -> **dy/dx= (3x +3∆x-3x) / ∆x

** -> **dy/dx= 3∆x / ∆x

**-> dy/dx=3 meaning derivative of function, f(x)=3x is ‘3’**

**Power rule of Derivatives: **

**Example: **What is the derivative of x^{4}?

** Here n=4, so dy/dx= 4x ^{4-1}**

** dy/dx=4x ^{3}**

**Example: **What is the derivative of 1/x^{3}**?**

** Here 1/x ^{3} can also be written as x^{-3}, so n=-3**

** dy/dx=-3x ^{-3-1} = -3x^{-4}**

**Example: **What is the derivative of 3x^{2}+x^{5}?

** Using the Sum rule, (f+g)’=f’ + g’**

** ->** d (3x^{2}+x^{5})/dx=3*2x^{2-1} +5*x^{5-1}

** -> 6x ^{1}+5x^{4}**

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