What is the derivative of this function?Please show how it can be done via power rule, and via product rule(2x-1)^2(X^2-9)

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embizze | High School Teacher | (Level 1) Educator Emeritus

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(1) Using only the product rule, find `d/(dx)[(2x-1)^2(x^2-9)]`

(a)Rewrite as `d/(dx)[(2x-1)(2x-1)(x^2-9)]`

Use the extended product rule `d/(dx)f*g*h=f'gh+fg'h+fgh'` where f,g, and h are differentiable functions of x.

Thus `d/(dx)[(2x-1)(2x-1)(x^2-9)]`




(b) Or rewrite as `d/(dx)[(2x-1)(2x-1)(x+3)(x-3)]` , but this is just more work. You would use `d/(dx)f*g*h*k=f'ghk+fg'hk+fgh'k+fghk'`

(2) Using the power rule `d/(dx)u^n=n(u^(n-1))(du)/(dx)` (Note the use of the chain rule):** we still use the product rule**







Either way the derivative is `16x^3-12x^2-70x+36`




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