1. Rewrite the expression in terms of logarithms:
Then differentiate with the chain rule (I'll use prime notation to save space; that is, the derivative of <em>y</em> is denoted <em>y' </em>)
2. Chain rule:
Since , we can cancel one factor of sine:
3. Chain rule:
4. If you're like me and don't remember the rule for differentiating logarithms of bases not equal to <em>e</em>, you can use the change-of-base formula first:
Then
So we have
and we can use the double angle identity and logarithm properties to condense this result:
5. Differentiate both sides:
6. Same as with (5):
7. Looks like
Compute the second derivative:
Set this equal to 0 and solve for <em>x</em> :