# Thread: find the slope of the curve

1. ## find the slope of the curve

The equation sin xy = y defines y implicitly as a function of x.
Find the slope y'(pi/3,1/2) at the point x=pi/3, y=1/2.

i know that y' = (ycos(xy))/(1-xcos(xy))

but i just dont know how to solve the problem when i plug in x and and y to find the slope

ty

2. Originally Posted by vtong
The equation sin xy = y defines y implicitly as a function of x.
Find the slope y'(pi/3,1/2) at the point x=pi/3, y=1/2.

i know that y' = (ycos(xy))/(1-xcos(xy))

but i just dont know how to solve the problem when i plug in x and and y to find the slope

ty
y=sin(xy) so $y'=\frac{y\cos{xy}}{1-x\cos{xy}}$ and plug in to get $y'=\frac{\frac{1}{2}\cos{\frac{\pi}{6}}}{1-\frac{\pi}{3}\cos{\frac{\pi}{6}}}$ which is the slope of your function

3. Originally Posted by vtong
The equation sin xy = y defines y implicitly as a function of x.
Find the slope y'(pi/3,1/2) at the point x=pi/3, y=1/2.

i know that y' = (ycos(xy))/(1-xcos(xy))

but i just dont know how to solve the problem when i plug in x and and y to find the slope

i.e. Plug in $\frac{\pi}{3}$ wherever you see an x, and $\frac{1}{2}$ whereever you see a y.
Note* $\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}$.