How do you find the derivative of #root6(x^5)#?

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Answer 1 · 2018-04-12T05:14:34

#=5/(6root(6)x)#

#f(x)=root(6)(x^5)=x^(5/6)#
#d/dx f(x)=5/6x^(5/6-1)#
#=5/6x^(-1/6)#
#=5/(6root(6)x)#

Answer 2 · 2018-04-12T05:16:11

Derivative of #root(6)x^5# is #5/(6root(6)x)#

The derivative of #x^n# is #nx^(n-1)#

As we can write #root(6)x^5=x^(5/6)#

#d/(dx)root(6)x^5=5/6x^(5/6-1)#

= #5/6x^(-1/6)#

= #5/6*1/root(6)x#

= #5/(6root(6)x)#