Derivative of $n/x$ My assignment asks me to calculate the derivative of:
$$y = \frac{9}{x} + 6 \sec x$$
My first step, it seems, should be to break the equation up and find the derivatives of $\frac{9}{x}$ and $6 \sec x$, which would be $1$ and $6(\sec x\tan x)$, respectively.
This would leave with $ 1 + 6(\sec x \tan x) $ as a final answer. However, the answer given in my book is $-\frac{9}{x^2} + 6\sec x\tan x $.
Obviously, I'm incorrect in my assumption that the derivative of $\frac{9}{x} = 1$, however I don't understand why. Can it be said that the derivative of any $\frac{n}{x} = \frac{n}{x^2}$?

Have you learned the power rule? It states that for all integers $k\neq 0$ (and actually real numbers), the derivative of $x^k$ is $kx^{k-1}$.
If we want to find the derivative of $\frac{n}{x}$, we can rewrite it as $nx^{-1}$, so its derivative must be $-nx^{-2}=-\frac{n}{x^2}$.
