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How do you find the derivative of #Y= ( 5x + 3 )( x - 7)^(-1/3)#?

1 Answer

Jun 3, 2015

In this way with the product rule:

#y'=5(x-7)^(-1/3)+(5x+3)(-1/3)(x-7)^(-1/3-1)=#

#=1/3(x-7)^(-4/3)*[3*5*(x-7)^(-1/3-(-4/3))-(5x+3)*1]=#

#=1/3(x-7)^(-4/3) * [15*(x-7)-5x-3]=#

#=1/3(x-7)^(-4/3)(10x+102)=#

#=2/3(x-7)^(-4/3)(5x+51)#.

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