Find the slopes of the tangent and the normal to the curve `x y=6` at `(1,\ 6)`

Answer

Slope of tangent at `(1,6)` is `-6`

Slope of normal `= 1 / 6`

Explanation

Given as `x y=6` at `(1,6)`

Differentiate using product rule
$$
\begin{aligned}
&\frac{d}{dx (x y)}=\frac{d}{dx (6)} \\
&\Rightarrow x \times \frac{d}{d x}(y)+y \frac{d}{d x}(x)=\frac{d}{d x}(5) \\
&\therefore \frac{d}{d x (\text { Constant })}=0 \\
&\Rightarrow x \frac{d y}{d x}+y=0 \\
...