Math Help - The Product Rule, am I on the right track?

1. The Product Rule, am I on the right track?

Hi all,

I've been asked to use the product rule to show that the function

$g(x)=(1+2sinx)e^{\frac{1}{2}x+cosx}$

has derivative

$g'(x)=\frac{1}{2}(4cos^{2}x+4cosx-3)e^{\frac{1}{2}x+cosx}$

have I started right with

$g'(x)=(2cosx)(e^{\frac{1}{2}x+cosx})+(1+2sinx)[(e^{\frac{1}{2}x+cosx})(\frac{1}{2}-sinx)]$

Many thanks all.

2. Re: The Product Rule, am I on the right track?

Looks okay to me. You have some algebra in your future.

3. Re: The Product Rule, am I on the right track?

It looks all right so far. Now you should distribute the product and use the trigonometrical identity to exchange sines for cosines.

4. Re: The Product Rule, am I on the right track?

Thank you both, I very much appreciate it. I will continue with it this evening.