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Evaluate the given functions.$$X(x, t)=-6 x t+x t^{2}-t^{3} ; \text { find } X(x,-t), \text { and } X(t, 2 x)$$

$X(x,-t)=6 x t+x t^{2}+t^{3}, X(t, 2 x)=-12 x t+4 x^{2} t-8 x^{3}$

Calculus 3

Chapter 29

Partial Derivatives and Double Integrals

Section 1

Functions of Two Variables

Partial Derivatives

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We want to evaluate a given function for X of x T equals negative six X T X T squared by the CQ. We wanna fly X of x negative T X of T two X. This question is testing your knowledge and multi variant functions in particular assessing our ability to evaluate such functions. Remember that To solve these functions, we have to solve identical single variable functions. That is. We simply plug in the indicator variables. For instance, for X X negativity, wherever we see X, we plug in X wherever we see T. We plug in negative T. So we then have X. X negative equals negative six times negative T plus extends dignity squared minus negative T. Cute. Let's have final solution six X T x T squared plus C. Cute. Then for X of T two X we have negative 16 cm two X plus TN two X squared minus two X. Cute. Or negative 12 T x plus 40 X squared minus eight execute

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