Partial Derivatives: Practice Problems

Determine the partial derivative of z with respect to x and then y for each of these functions.

1. z = 3x^{2}y + y^{2} + 1/x

2. z = 10xy^{2} – y^{3}/x – 5x^{2}

3. z = x^{2} y^{2} + x^{2}/y^{2} + x^{2} + y^{2}

4. z = y sin x + x^{2}sin^{2}y + xy sin(y^{2})