Question

Differentiate. F(x) = (x3 - 3)2/3 2x f'(x) - 3 8 O f'(x) = 3 8 2x2 f'(x) 3 VX3 -8 f(x) 3 V3-8​

Answer 1

`f'(x) = \frac{2{x}^(2)}{ \sqrt[3]{( {x}^(3) - 8) } }`

Explanation:

`f(x) = ( {x}^(3) - 8)^{ (2)/(3) } \\ \\ f'(x) = (2)/(3) ( {x}^(3) - 8)^{ (2)/(3) - 1 } (3 {x}^(2) - 0) \\ \\ f'(x) = (2)/(3) ( {x}^(3) - 8)^{ (2 - 3)/(3) } * 3 {x}^(2) \\ \\ f'(x) = 2{x}^(2)( {x}^(3) - 8)^{ ( - 1)/(3) } \\ \\ f'(x) = \frac{2{x}^(2)}{( {x}^(3) - 8)^{ ( 1)/(3) } } \\ \\ \huge \red{ \boxed{ f'(x) = \frac{2{x}^(2)}{ \sqrt[3]{( {x}^(3) - 8) } } }}`