Question

How do you differentiate `x^sqrt5+sqrt(5x)`?

Answer 1

`dy/dx=sqrt5*x^(sqrt5-1)+sqrt5/(2sqrtx).`

Explanation:

`d/dx{x^(sqrt5)+sqrt(5x)},`

`=d/dx{x^sqrt5}+d/dx{sqrt5*x^(1/2)},`

`=sqrt5*x^(sqrt5-1)+sqrt5*d/dx{x^(1/2)},`

`=sqrt5*x^(sqrt5-1)+sqrt5{1/2x^((1/2)-1)},`

`=sqrt5*x^(sqrt5-1)+sqrt5{1/2x^(-1/2)}.`

`rArr dy/dx=sqrt5*x^(sqrt5-1)+sqrt5/(2sqrtx).`