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1.  If \(\sin(xy) = y\), find \(\frac{dy}{dx}\)

a.  \(\frac{dy}{dx} = \frac{y\cos(xy)}{1-x\cos(xy)}\)

b.  \(\frac{dy}{dx} = \frac{y\cos(xy)}{1+x\cos(xy)}\)

c.  \(\frac{dy}{dx} = \frac{-y\cos(xy)}{1+x\cos(xy)}\)

d.  \(\frac{dy}{dx} = \cos(xy)\)

e.  \(\frac{dy}{dx} = y\cos(xy)\)

2.  Find \(\frac{dy}{dx}\) if \(x^3y + x + y^2 = 11\).

a.  \(\frac{dy}{dx} = \frac{-3x^2y-1}{x^3+2y}\)

b.  \(\frac{dy}{dx} = \frac{x^3+2y}{-3x^2y-1}\)

c.  \(\frac{dy}{dx} = 3x^2 + 1 + 2y\)

d.  \(\frac{dy}{dx} = 3x^2y + x^3 + 1 + 2y\)

e.  \(\frac{dy}{dx} = 3x^2y + 1 + 2y\)

3.  Find the equation of the tangent line to the curve \(x\sin y = 2 y\) at the point \( (\pi, \frac{\pi}{2}\)

a.  \( y = 2x - \frac{\pi}{2}\)

b.  \( y = 2x - \frac{3\pi}{2}\)

c.  \( y = \frac{1}{2} x - \frac{\pi}{2}\)

d.  \( y = \frac{1}{2} x \)

e.  \( y = x - \frac{\pi}{2}\)