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Find 4 ( (Tepavrial dexivatr J Jivcn functiehS hCXY) x3 4*Yte6) 9 CxLYZLe 2xx242 !Xe (provide partial f Xul2 )...

Question

Find 4 ( (Tepavrial dexivatr J Jivcn functiehS hCXY) x3 4*Yte6) 9 CxLYZLe 2xx242 !Xe (provide partial f Xul2 )

Find 4 ( ( Te pavrial dexivatr J Jivcn functiehS hCXY) x3 4*Y te 6) 9 CxLYZLe 2xx2 42 ! Xe (provide partial f Xul2 )



Answers

In Exercises $43-46,$ compute the given partial derivatives. $$ f(x, y)=3 x^{2} y+4 x^{3} y^{2}-7 x y^{5}, \quad f_{x}(1,2) $$

Mhm. In this problem we want to find the specified process revenue. That's why of zero pi or do a bit of a destructive Y. At the 00.0 pi for F. Of X. Y equals sine X squared minus Y. This question challenges our understanding of differentiation and multi variant functions. In order to solve, we must understand that president is quite a few single variable differentiation techniques to respect our differences variable, treating other variables as conscience Along the way as an example. We differentiate X. Y. With respect to X. Y. And Z. Obtaining solution Y X zero respectively. With an example in the explanation given above, we can proceed to logically solve. What we're going to do is first find F. Y and then plug in the 00.0. So F Y. Is by the chain rule cause an X squared minus Y. Times zero minus one. Or negative coastline experimenters. Why thus F. Y. Of zero pi is negative coastline of zero minus pi which is negative coastline of negative pi, which is negative negative one equals positive one.

Yeah. To find the partial derivative with respect to ACT, we treat white as a constant and differentiate with respect to ACT shows uh derivative of the inverse tangent function. Als Yeah, while over one plus fire ax minus seven y squared and videos. The chain rule the derivative with respect to flex. As for to find the partial derivative with respect to why retreat acts as a constant. And differentiate with respect to one. So the derivative of the inverse tangent function as while over one plus fires miners seven y squared. Here we use the chain rule, the derivative of minus seven Y. He calls minus seven.

In this problem we want to find the first partial derivatives of a given function F is equal to the tangent of X. Y. Q. This question is challenge your understanding of differentiation of both. High very functions in order to solve, we need to understand that to find the partial derivatives. Were you single variable differentiation techniques with respect to our differential variable treating other variables constants along the way. So to demonstrate the staff and differentiated the function X. Y. With respect to X, Y. Z. Near the green line differentiating X, Y. X is one times Y or Y differentiating Xy perspective. Why is X times one or X? And differential reflects easy because there is no variables in the equation or function is simply zero. So this logic in hand, we can proceed to solve the first part of this research for FX and Fy because that's like you get inside the tangent, we have to use the tangent derivatives. You can square in the chain rule. Thus fxx, you can't squared X Y cube times. Why cute? Which is seeking an X Y cube? Thus fy is even below. But first let's note that we have to have a factor of Y cube on the second square to solve correctly. Thus we have fy below sea. Can squared X Y Q. By the chain. Will three y squared? Make sure we include our factor of X. Thus we have solution three Y squared X squared X. Y, cute Again, make sure we don't miss out on the other variable and different cheating. So we're like the three xy squared C squared X. Like huge.

Uh huh. In this problem we want to find the first pressure to rivers of a given function as equals the arc tangent or inverse tangent of X. Y square. This question is challenging understanding of differentiation of multi variant functions. In order to evaluate, we could use partial derivatives which use single variable differentiation techniques, respecting differences, variable treating other variables along the way demonstrate this principle, I differentiate the function X, Y or in fact of variables X, Y and Z below derivatives with respect to X and Y or Y and acts respectively as a preventive factor, Z is zero because there is no zero. The function with this lot to get ahead. We can easily solved. We we look for Fx and Fy is our first derivatives. So using the archangel derivative in the chain rule, we have F X equals 1/1 plus x squared y squared square times one Y squared equals y squared over one plus x squared y to the fourth. Similarly, we find F y equals 1/1 plus x, Y squared squared times x, two times two Y, or two, Y x over one plus X squared Y to the fourth.


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