Homework SourseThe equation sin xy y defines y implicitly as a function of
The equation sin xy = y defines y implicitly as a function of x.
y\'(pi/3,1/2) at the point x=pi/3, y=1/2.
Step 1 - Implicitly differentiate the equation with respect to x to find a formula for y \' in terms of x and y.
y \'(x,y) =
y\'(pi/3,1/2) at the point x=pi/3, y=1/2.
Step 1 - Implicitly differentiate the equation with respect to x to find a formula for y \' in terms of x and y.
y \'(x,y) =
Solution
sin(xy) = y
differentiate wrtx
cos(xy)[y + xy\'] = y\'
ycos(xy + xcos(xy)y\' = y\'
y\'(1-xcos(xy)) = ycos(xy)
y\' = ycos(xy)/(1-xcos(xy))
at x = pi/3, y = 1/2
y\' = 1/2cos*(pi/6)/[1-pi/3cos(pi/6)]
y\' = (1/2*3/2)/[1-/23]
y\' = 3/[4 - 2/3]
