`g(x) = (x^2 + 1)(x^2 + 2)^6` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 18 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsenviro | College Teacher | (Level 1) Educator Emeritus

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Using the product rule for derivatives:

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

`g'(x) = d/dx[(x^2+1)(x^2+2)^6]= 2x*(x^2+2)^6 + (x^2+1)*6(x^2+2)^5*2x`

`= (x^2+2)^5 * 2x*[(x^2+2)+6*(x^2+1)] = 2x*(7x^2+8)(x^2+2)^5`

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