`f(x) = 20root(5)(x)` Find the second derivative of the function.

Textbook Question

Chapter 2, Review - Problem 48 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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Note:- If y = x^n ; where n = constant ; then dy/dx = n*{x^(n-1)}

Now, 

`y = 20*x^(1/5)`

`y' = 20*(1/5)*x^{(1/5)-1}`

`or, y' = 4*x^(-4/5)`

`thus, y'' = 4*(-4/5)*x^{(-4/5)-1}`

`or, y'' = -(16/5)*x^(-9/5)`

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