Answer: its 62
Step-by-step explanation:
Isolate the radical, then raise each side of the equation to the power of its index.
Answer:
![f(x) =\sqrt{x} sin (x)](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%5Csqrt%7Bx%7D%20sin%20%28x%29)
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)](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%20%28f%28x%29%2A%20g%28x%29%29%20%3D%20f%27%28x%29%20g%28x%29%20%2Bf%28x%29%20g%27%28x%29)
Where
and
And replacing we have this:
![f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)](https://tex.z-dn.net/?f=%20f%27%28x%29%3D%20%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D%20sin%20%28x%29%20%2B%20%5Csqrt%7Bx%7Dcos%28x%29)
Step-by-step explanation:
We assume that the function of interest is:
![f(x) =\sqrt{x} sin (x)](https://tex.z-dn.net/?f=%20f%28x%29%20%3D%5Csqrt%7Bx%7D%20sin%20%28x%29)
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)](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd%7D%7Bdx%7D%20%28f%28x%29%2A%20g%28x%29%29%20%3D%20f%27%28x%29%20g%28x%29%20%2Bf%28x%29%20g%27%28x%29)
Where
and
And replacing we have this:
![f'(x)= \frac{1}{2\sqrt{x}} sin (x) + \sqrt{x}cos(x)](https://tex.z-dn.net/?f=%20f%27%28x%29%3D%20%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D%20sin%20%28x%29%20%2B%20%5Csqrt%7Bx%7Dcos%28x%29)
Answer:
The answer is 5
Step-by-step explanation: