Question

What is the derivative of this function `sin x^(1/2)`?

Answer 1

`cos(x^(1/2))/(2x^(1/2)`

Explanation:

differentiate using the `color(blue)"chain rule"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(a/a)|)))....(A)`

let `u=x^(1/2)rArr(du)/(dx)=1/2x^(-1/2)`

and `y=sin(u)rArr(dy)/(du)=cos(u)`

substitute these values into (A) changing u into terms of x

`rArrdy/dx=cos(u)xx1/2x^(-1/2)=cos(x^(1/2))/(2x^(1/2)`