How do you find #(d^2y)/(dx^2)# given #y=root3(x)#?

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Answer 1 · 2016-10-31T02:54:44

#(d^2y)/dx^2 = -2/(9x^(5/3))#

The notation #(d^2y)/dx^2# means to find the 2nd derivative.

So, we differentiate once, and we differentiate that result again.

#y = root(3)(x) -> y = x^(1/3)#

#y' = 1/3x^(-2/3) #

The second derivative is found by differentiating the first derivative.

#y'' = 1/3(-2/3)x^(-5/3) = -2/9x^(-5/3) = -2/(9x^(5/3))#

Hopefully this helps!