Find the derivatives of the following:ex=e(x-y) - Mathematics

Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`

Sum

`sqrt(x) = "e"^((x - y))`

Squarting on both sides

`(sqrt(xy))^2 = ["e"^((x - y))]^2`

xy = `"e"^(2(x - y))` .......(1)

`x * ("d"y)/("d"x) + y * 1 = "e"^(2(x - y)) xx 2(1 - ("d"y)/("d"x))`

`x ("d"y)/("d"x) + y = 2"e"^(2(x - y)) - 2"e"^(2(x - y)) ("d"y)/("d"x)`

`x ("d"y)/("d"x) + 2"e"^(2(x - y)) ("d"y)/("d"x) = 2"e"^(2(x - y)) - y`

`[x + 2"e"^(2(x - y))] ("d"y)/("d"x) = 2"e"^(2(x - y)) - y`

`("d"y)/("d"x) = (2"e"^(2(x - y)) - y)/(x + 2"e"^(2(x - y))`

`("d"y)/("d"x) = (2xy - y)/(x + 2xy)`

By equation (1)

`("d"y)/("d"x) = (y(2x - 1))/(x(1 + 2y))`

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Chapter 10: Differential Calculus - Differentiability and Methods of Differentiation - Exercise 10.4 [Page 176]

Chapter 10 Differential Calculus - Differentiability and Methods of Differentiation
Exercise 10.4 | Q 3 | Page 176

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