the slope is 0.288
Explanation
Step 1
given
[tex]xcosy=1[/tex]
a) find the implicit derivate
[tex]\begin{gathered} xcosy=1 \\ cosy-xsiny*y^{\prime}=0 \\ y^{\prime}=\frac{-cosy}{-xsiny} \\ y^{\prime}=\frac{cosy}{xs\imaginaryI ny} \end{gathered}[/tex]
b), now ,Plug x value of the indicated point into f '(x) to find the slope at x
[tex]\begin{gathered} y^{\prime}=\frac{cosy}{xs\imaginaryI ny} \\ y^{\prime}=\frac{cos(\frac{\pi}{3})}{2sin(\frac{\pi}{3})}= \\ y^{\prime}=0.288 \end{gathered}[/tex]
so, the slope is 0.288
I hope this helps you
