Find the derivative of the function at $P_0$ in the direction of $u$.$$f(x,\, y,\,z) = \tan^{-1}\left ( \frac{5x}{9y+2z} \right ),\,\,\, P_0(7,\,0,\,0),\,\,\, u = 12i - 3j+4k$$
I understand how to find directional derivatives, but I keep getting the wrong answer. I completed the partials for each and double checked my work with wolfram, and then I multiplied each by its corresponding direction, 12,-3,4. I get 0 for the partial of x portion, ${27}/{35}$ for the y portion, and $8/35$ for the z portion. Any clues where I am going wrong?