How do you find the derivative of #(x^(2/3 ))(8-x)#?

1 Answer
Jun 29, 2015

Answer:

#( d (8x^(2/3) - x^(-1/3)))/(dx) = 1/(3root(3)(x)) *(16+1/x)#

Explanation:

#(x^(2/3))(8-x)#
#color(white)("XXXX")##=8x^(2/3) - x^(-1/3)#

#( d (8x^(2/3) - x^(-1/3)))/(dx) = color(red)((d (8x^(2/3)))/(dx)) - color(blue)((d (x^(-1/3)))/(dx))#

#color(white)("XXXX")##=color(red)( 2/3*8x^-(1/3)) - color(blue)((-1/3)x^(-4/3))#

#color(white)("XXXX")##= 16/(3root(3)x) + 1/(3(root(3)(x))^4)#

#color(white)("XXXX")##= 16/(3root(3)x) + 1/(3(x*root(3)(x)))#

#color(white)("XXXX")##= 1/(3root(3)(x)) *(16+1/x)#