Answer:
[tex] f(x) =\sqrt{x} sin (x)[/tex]
And on this case we can use the product rule for a derivate given by:
[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]
Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]
And replacing we have this:
[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]
Step-by-step explanation:
We assume that the function of interest is:
[tex] f(x) =\sqrt{x} sin (x)[/tex]
And on this case we can use the product rule for a derivate given by:
[tex] \frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)[/tex]
Where [tex] f(x) =\sqrt{x}[/tex] and [tex] g(x) =sin (x)[/tex]
And replacing we have this:
[tex] f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)[/tex]
