Question

Cual es la derivada de ()=√x sin

Answer 1

Answer:

$f(x) =\sqrt{x} sin (x)$

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

$\frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)$

Where $f(x) =\sqrt{x}$ and $g(x) =sin (x)$

And replacing we have this:

$f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)$

Step-by-step explanation:

We assume that the function of interest is:

$f(x) =\sqrt{x} sin (x)$

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

$\frac{d}{dx} (f(x)* g(x)) = f'(x) g(x) +f(x) g'(x)$

Where $f(x) =\sqrt{x}$ and $g(x) =sin (x)$

And replacing we have this:

$f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)$