f(x)=x^2/3 (2-x) = x^2/3 (2-x)

Question

find 1st and 2nd derivative for

x to the 2/3 * (2-x) =  x to the 2/3 * (2-x)

sorry I didn't clarify

Answer 1

f(x) = x^2/3(2 - x)

 

I would first distribute to make it easier to derive (otherwise we would have to use the product rule and that can get messy).

 

f(x) = 2x^2/3 - x^5/3     (remember x is really x¹ or x^3/3 in this case, so x^2/3 times x^3/3 is x^5/3)

 

Now use the power rule:

 

f'(x) = 2(2/3)x^-1/3 - (5/3)x^2/3 = (4/3)x^-1/3 - (5/3)x^2/3

 

Now do the same thing to f'(x) to get f"(x):

 

f"(x) = (4/3)(-1/3)x^-4/3 - (5/3)(2/3)x^-1/3 = (-4/9)x^-4/3 - (10/9)x^-1/3