Question

How would you find the first derivative of `f(x) = (5-x)x^(2/3)`?

Answer 1

I would use the Product Rule:
`f'(x)=-1*x^(2/3)+(5-x)2/3x^(-1/3)=`
`=-x^(2/3)+10/3x^(-1/3)-2/3x^(2/3)=`
`=-x^(2/3)[1+2/3]+10/3x^(-1/3)=`
`=-x*x^(-1/3)[5/3]+10/3x^(-1/3)=`
`=-5(x-2)/(3root3(x))`