`y = root(3)(6x^2 + 1)` Find the derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 13 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace's profile pic

mathace | (Level 3) Assistant Educator

Posted on

Given `y=root(3)(6x^2+1)`

Rewrite the function as `y=(6x^2+1)^(1/3)`

Find the derivative using the Chain Rule.

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

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

`y'=(4x)/(6x^2+1)^(2/3)`

`y'=(4x)/root(3)((6x^2+1)^2)`

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kandukurimaths's profile pic

kandukurimaths | Student, Graduate | (Level 1) Honors

Posted on

y=`root(3)(6x^2+1)`  

 `y^3` =6+1 

apply derivative both side with respect x

using chain rule

 f(g(x)) = f'(g(x))g'(x)

3`y^2`(dy/dx)=12x+0

dy/dx=4x/`y^2`

dy/dx=4x/((6x^2+1)^(2/3))``

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