Question

Cual es la derivada de ()=√x sin

Answer 1

`f(x) =√(x) sin (x)`

And on this case we can use the product rule for a derivate given by:

`(d)/(dx) (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)`

Where
`f(x) =√(x)` and
`g(x) =sin (x)`

And replacing we have this:

`f'(x)= (1)/(2√(x)) sin (x) + √(x)cos(x)`

Explanation:

We assume that the function of interest is:

`f(x) =√(x) sin (x)`

And on this case we can use the product rule for a derivate given by:

`(d)/(dx) (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)`

Where
`f(x) =√(x)` and
`g(x) =sin (x)`

And replacing we have this:

`f'(x)= (1)/(2√(x)) sin (x) + √(x)cos(x)`