Question

How do you differentiate `y=sqrt(x + 1)/root3( x^4)`?

Answer 1

`(3(x+1)^(-1/2)*x^(4/3)-8(x+1)^(1/2)*x^(1/3))/(6x^(8/3))`

Explanation:

By the Quotient rule we get
`(1/2*(x+1)^(-1/2)*x^(4/3)-2(x+1)^(1/2)*4/3*x^(1/3))/x^(8/3)`
Multiplying numerator and denominator by `6`
`(3(x+1)^(-1/2)*x^(4/3)-8(x+1)^(1/2)*x^(1/3))/(6*x^(8/3))`