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

Answer:

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

Step-by-step explanation:

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