h(theta)= 9sec(theta)+9e^(theta)cot(theta)
h'(theta)=d/dtheta(9sec(theta)) + d/dtheta(9e^(theta)cot(theta))
?= 9sec(theta) 9 tan(theta)+ ..... ?
Since $\displaystyle \theta$ is a constant, we are not going to explicitly differentiate it, since $\displaystyle dk/dx$, where k is a constant, is 0. For the first term $\displaystyle 9sec(\theta)$, remember that $\displaystyle d/dx * sec(x) = sec(x)tan(x)$.
For the second term, remember that $\displaystyle d/dx e^x = dx e^x$. So if $\displaystyle x = \theta cot(\theta)$, then $\displaystyle dx = \theta * -csc^2(\theta)$.