Question

Using the Product Rule, use the Product Rule to find the derivative of the function.

Answer 1

Given the following function:

$g(x)=\sqrt{x}*sin\text{ }x$

We will use the Product Rule to find the derivative of the function.

The product rule is as follows:

$\begin{gathered} g(x)=m*n \\ g^{\prime}(x)=m^{\prime}*n+m*n^{\prime} \end{gathered}$

For the given function:

$\begin{gathered} m=\sqrt{x}\rightarrow m^{\prime}=\frac{1}{2\sqrt{x}} \\ \\ n=sin\text{ }x\rightarrow n^{\prime}=cos\text{ }x \end{gathered}$

So, the derivative of the function will be as follows:

So, the answer will be

$g^{\prime}(x)=\frac{sin\text{ }x}{2\sqrt{x}}+\sqrt{x}\text{ }cos\text{ }x$