Question

How do you find the derivative of `sqrt(x)/(x^3+1)`?

Answer 1

`(df)/(dx)=(1-5x^3)/(2sqrtx(x^3+1)^2)`

Explanation:

As `f(x)=sqrtx/(x^3+1)`, using quotient rule,

`(df)/(dx)=(d/(dx)sqrtx xx (x^3+1)-d/(dx)(x^3+1)xx sqrtx)/(x^3+1)^2`

= `(1/(2sqrtx)xx(x^3+1)-3x^2 xx sqrtx)/(x^3+1)^2`

= `(x^3+1-6x^3)/(2sqrtx(x^3+1)^2)`

= `(1-5x^3)/(2sqrtx(x^3+1)^2)`