How do you differentiate #f(x)= (x^2+1)(5x^4+3^2+2x) # using the product rule?

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Answer 1 · 2018-05-07T08:57:14

#color(brown)(f'(x) = 30x^5 + 20x^3 + 6x^2 + 18x + 2#

#f(x) = (x^2 + 1) * (5x^4 + 2x + 3^2)#

#Let " "u = ((x^2 + 1), v = (5x^4 + 2x + 9)#

#(du)/(dx) = (d/(dx)) (x^2 + 1) = 2x#

#(dv) / (dx) = d/(dx) (5x^4 + 2x + 9) = 20x^3 + 2#

#f'(x) = v (du)/(dx) + u (dv)/(dx)#

#f'(x) = (5x^4 + 2x + 9) * 2x + (x^2 + 1) * (20x^3 + 2)#

#=> 10x^5 + 4x^2 + 18x + 20x^5 + 2x^2 + 20x^3 + 2#

#color(brown)(=> 30x^5 + 20x^3 + 6x^2 + 18x + 2#