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

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Answer 1 · 2016-07-29T13:09:30

#f'(x) = x(8x^2+9x+2)#

The product rule states that

#d/(dx)(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)#

#f(x) = 2x+1 and g(x) = x^3 + x^2#

#implies f'(x) = 2 and g'(x) = 3x^2 + 2x#

#f'(x)g(x) + f(x)g'(x) = 2x^3 + 2x^2 + (2x+1)(3x^2+2x)#

#=2x^3 + 2x^2 + 6x^3 + 4x^2 + 3x^2 + 2x = 8x^3 + 9x^2 + 2x#

#=x(8x^2+9x+2)#