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

Question

1455 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-25T17:05:00

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

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

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

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

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

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

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

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