Find the second derivative:

$\displaystyle

f(x) = \frac{1}{x} + \tan(x)

$

$\displaystyle

f'(x) = -x^{-2} + \sec^2(x)

$

$\displaystyle

f"(x) = 2x^{-3} + 2\sec(x)\sec(x)\tan(x)

$

$\displaystyle

f"(x) = \frac{2}{x^3} + 2\sec^2(x)\tan(x)

$

My teacher got $\displaystyle f"(x) = \frac{2}{x^3} + 2\sec^2(x)\tan^2(x)$ but I think she just put the tanx in for u on accident... Is my second derivative correct?