F⁾(x)=(x²+∛(x²))⁾= 2x+ 2/3 *x²/₃⁻¹=2x +2/(3x¹/₃)
________________________________________________
(х+√х) (х+√х)⁾*(х-√х)-(х-√х)⁾*(х+√х)
f⁾(x)= ----------- = ------------------------------------ =
(х-√х) (х-√х)²
(1+ 1/(2√х))*(х- √х) - (1- 1/(2√х))* (х +√х)
= ------------------------------------------------------------ =
(х-√х)²
х+ х/(2√х) - √х- (√х/2√х) -(х- х/(2√х)+ √х- √х/(2√х))
= -------------------------------------------------------------------------- =
(х-√х)²
х+ х/(2√х) - √х- (√х /(2√х)) -х+ х/(2√х)- √х +√х/(2√х))
= --------------------------------------------------------------------
(х-√х)²
√х/2 +√х/2 -2√х √х- 2√х -√х
= ------------------------ = ----------------- = ----------------
(х-√х)² (х-√х)² (х-√х)²
____________________________________________________
f⁾(x)=(x³ +∛x⁵ )⁾=3x²+ 5/3 *x⁵/₃⁻¹ = 3x²+ (5x²/₃)/3