Question

How do you differentiate `u=root5(t)+4sqrt(t^5)`?

Answer 1

`(du)/(dt)=1/(5t^(4/5))+2/sqrt(t^5)`

Explanation:

`u=t^(1/5)+4(t^5)^(1/2)`

If `y=ax^n` then the derivative, `dy/dx=nax^(n-1)`

Using this, `(du)/(dt)=1/5t^(-4/5)+4(1/2)(t^5)^(-1/2)=1/(5t^(4/5))+2/sqrt(t^5)`