f(x) = 2x-tan(x)

When is f concave down? I know that when the second derivative is negative, the graph is concave down, so f''(x) = -2sin(x)/(cos(x))^3, right?

When is that negative?

Also,

lim as x->0

sin(5x)/x

where 5x = theta

and how do I use that result to find the derivative of sin(5x)?

Any help appreciated.