What is the derivative of #(3x+1)(3x^2+5)#?

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Answer 1 · 2018-03-07T07:29:38

#f'(x) = 27x^2 +6x +15#

Given: Find derivative of #(3x+1)(3x^2+5)#

Use the product rule: #(uv)' = uv' + v u'#

Let #u = 3x +1; " " u' = 3#

#" "v = 3x^2 +5; " " v' = 6x#

#f'(x) = (3x+1)(6x) + (3x^2 +5)(3)#

Simplify:
#f'(x)= 18x^2 +6x + 9x^2 +15#

#f'(x) = 27x^2 +6x +15#