Verified Answer :

Kerbal27

d/dx sqrt(x) sin(x) = \(d/dx \sqrt{x}*sin(x) + d/dx*sin(x) \sqrt{x}\)
= \(\frac{1}{2 \sqrt{x}} * sin(x) + cos(x)* \sqrt{x}\)
=\(\frac{sin(x)+2xcos(x)}{2 \sqrt{x}}\)

altavistard

You are finding the derivative of the square root of a product:  

y = sqrt ( x sin x )    =    ( x sin x )^(1/2)       This is a power function!

Apply the Power Rule with Chain Rule.  This involves two main steps:

1.  Find the derivative of ( x sin x)^(1/2) with respect to (x sin x).  This is

(1/2) (x sin x)^(-1/2).

2.  Multiply this result by the derivative of x sin x        (which is a PRODUCT).

Can you finish this?  Hint:  You must now apply the product rule.

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