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Find the indicated partial derivative. f(x, y) = y \sin^{-1}(xy); f_y(2, \frac{1}{4}) f_y(2,...

Question:

Find the indicated partial derivative.

{eq}f(x, y) = y \sin^{-1}(xy); f_y(2, \frac{1}{4}) {/eq}

{eq}f_y(2, \frac{1}{4}) {/eq} =

Partial Derivatives:

We compute for the partial derivative of a function similar to the total differential. We still follow the chain rule, product rule and quotient rule. However, for partial derivatives, we don't allow the other variables to vary, so we treat them as constants.

Answer and Explanation:

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We first find the expression for the partial derivative of the function.

{eq}\begin{align} f(x, y) &= y \sin^{-1}(xy)\\ f_y(x,y) &= y...

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Partial Derivative: Definition, Rules & Examples

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Chapter 18 / Lesson 12
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When a function depends on more than one variable, we can use the partial derivative to determine how that function changes with respect to one variable at a time. In this lesson, we use examples to define partial derivatives and to explain the rules for evaluating them.


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