`f(x) = (4x^3 + 3x^2)/x` Find the derivative of the function.

Textbook Question

Chapter 2, 2.2 - Problem 43 - Calculus of a Single Variable (10th Edition, Ron Larson).
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kalau | (Level 2) Adjunct Educator

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Use the quotient rule to solve this question.  The formula is:

`f'(x) = (BT' - TB')/ B^2`

Where B and T are bottom function and top function, respectively.

`B= x`

`B'=1`

`T=4x^3+3x^2`

`T'= 12x^2+6x`

Substitute all into the formula.

`f'(x)= ((x)(12x^2+6x)-(4x^3+3x^2)(1))/x^2`

Simplify the equation.

`f'(x)= (12x^3+6x^2-4x^3-3x^2)/x^2`

Combine like-terms and divide each term by `x^2` .

`f'(x)= (8x^3+3x^2)/x^2= 8x+3`

The answer is:  `f'(x)=8x+3`

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