Question

Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.

Answer 1

the slope is 0.288

Step-by-step explanation

Step 1

given

`xcosy=1`

a) find the implicit derivate

`\begin{gathered} xcosy=1 \\ cosy-xsiny*y^(\prime)=0 \\ y^(\prime)=(-cosy)/(-xsiny) \\ y^(\prime)=(cosy)/(xs\imaginaryI ny) \end{gathered}`

b), now ,Plug x value of the indicated point into f '(x) to find the slope at x

`\begin{gathered} y^(\prime)=(cosy)/(xs\imaginaryI ny) \\ y^(\prime)=(cos((\pi)/(3)))/(2sin((\pi)/(3)))= \\ y^(\prime)=0.288 \end{gathered}`

so, the slope is 0.288

I hope this helps you