Detail solution

Apply the product rule:
; to find :

The derivative of sine is cosine:
; to find :

The derivative of cosine is negative sine:
The result is:

Now simplify:
The answer is:
The first derivative
[src]
$$ \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}$$
The second derivative
[src]
$$ 4 \sin{\left(x \right)} \cos{\left(x \right)}$$
The third derivative
[src]
/ 2 2 \
4*\sin (x)  cos (x)/
$$4 \left(\sin^{2}{\left(x \right)}  \cos^{2}{\left(x \right)}\right)$$