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Differentiation FormulaDefinition –  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! 

Differentiation Formula Differentiation online assignment help

arrowExample: 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’

 

red arrowPower rule of Derivatives: 

exponent differentiation Differentiation Assignment Help

 

Blue ArrowExample: What is the derivative of x4?

                        Here n=4, so dy/dx= 4x4-1

                                 dy/dx=4x3

 

Blue ArrowExample: What is the derivative of 1/x3?

                        Here 1/x3 can also be written as x-3, so n=-3

                                      dy/dx=-3x-3-1 = -3x-4

 

dark blue arrowExample: What is the derivative of 3x2+x5?

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

                                     -> d (3x2+x5)/dx=3*2x2-1 +5*x5-1

                                     ->   6x1+5x4

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