CPM Homework Help : CALC Problem 9-65

Compute without a calculator No calculator! Find the slope of the curve $x$ cos $y = xy + 1$ at the point $(1, 0)$ .

Step 1:

$\frac{d}{dx}x\operatorname{cos}(y)=\frac{d}{dx}\Big(xy+1)\Big)$
$\operatorname{cos}(y)-x\operatorname{sin}(y)y^\prime=y+xy^\prime$

Step 2:

Solve for $y^\prime$ .

Step 3:

Evaluate the equation from step 2 for $x = 1$ and $y = 0$ .