Question

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

Answer 1

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)`.