# 022 Sample Final A, Problem 1

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Find all first and second partial derivatives of the following function, and demostrate that the mixed second partials are equal for the function

Foundations: |
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1)Which derivative rules do you have to use for this problem? |

2)What is the partial derivative of xy, with respect to x? |

1)You have to use the quotient rule, and product rule. The quotient rule says that , so . The product rule says . This means |

2) The partial derivative is y, since we treat anything not involving x as a constant and take the derivative with respect to x. So |

**Solution:**

Foundations: |
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The word 'marginal' should make you immediately think of a derivative. In this case, the marginal is just the partial derivative with respect to a particular variable. |

The teacher has also added the additional restriction that you should not leave your answer with negative exponents. |