Limits and Derivatives

Limits and Derivatives

Question

Find the derivative of the following :

(5x3+3x+1)(x-1)

Answer

Let        y = (5x+3x -1) (x-1)
differentiating both sides w.r.t. x, we  get
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       space space space space space space space space space space space space space space equals space left parenthesis 5 straight x cubed plus 3 straight x minus 1 right parenthesis straight d over dx left parenthesis straight x minus 1 right parenthesis plus left parenthesis straight x minus 1 right parenthesis straight d over dx left parenthesis 5 straight x cubed plus 3 straight x minus 1 right parenthesis
                 =(5x+3x -1) (1-0)+(x-1)(5x+3 -0) 
                 = 5x+3x -1+15x+3x -3
                 = 20x-15x+ 6x -4

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