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Given z = f(x,y), x = x(u,v), y =y(u,v) , with x(2,2) =1, y(2,2)=4 , calculate z_u(2,2) in...

Question:

Given {eq}z = f(x,y), x = x(u,v), y =y(u,v) {/eq}, with {eq}x(2,2) =1, y(2,2)=4 {/eq}, calculate {eq}z_u(2,2) {/eq} in terms of some of the values : {eq}f_x(2,2) =a, f_y(2,2) =d, x_u(2,2) = q, y_u(2,2)=r, f_x(1,4) = p, f_y(1,4) =1, x_v(2,2) = b, y_v(2,2) = c {/eq}

Partial Derivatives:

Partial derivatives find the instantaneous rate of change of a multivariable function in terms of a singular variable alone, where as the other input variable in the function are treated as constants.

Answer and Explanation: 1

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Given: {eq}z = f(x,y), x = x(u,v), y =y(u,v) \\ x(2,2) = 1, y(2,2) = 4 \\ f_x(2,2) = a, f_y(2,2) = d, x_u(2,2) = q, y_u(2,2) = r, f_x(1,4) = p,...

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Partial Derivative: Definition, Rules & Examples

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Chapter 18 / Lesson 12
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What is a Partial Derivative? Learn to define first and second order partial derivatives. Learn the rules and formula for partial derivatives. See examples.


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