I'm currently self learning multivariable calculus using Serge Lang Calculus of several variables book.
yesterday night,I stumbled on of the exercise on chapter 'Directional Derivative'.
The question look straightforward, I believe I may missed something very obvious.
The exercise in question as below....
In what direction are the following functions of r increasing most rapidly at the given point?
$\frac{x}{\|r\|^\frac{3}{2}}$ at $(1,-1,2)$ $(r=(x,y,z))$
the answer in the books is given as
$\left(\frac{9}{2.6^{7/4}},\frac{3}{2.6^{7/4}},-\frac{6}{2.6^{7/4}}\right)$ or also (3,1,-2)
i try this as $\frac{x}{({x^2+y^2+z^2})^\frac{5}{4}}$ and then use chain rule and quotient rule but came nowhere near the answer.
I been pulling my hair all night on this.