Question

find ds/dx for the curve find the DS by DX for the curve y square is equal to 4 a x ​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer:

The correct answer is : √(1 + a^2/x)

Step-by-step explanation:

To understand how the distance between two points on a curve y^2 = 4ax changes, we need to find an equation that tells us how the y-coordinate changes as the x-coordinate changes. We can do this by  taking the square root of both sides of the equation and considering only the positive root. Then, we can use calculus, to find how the y-coordinate changes with respect to the x-coordinate.

y = ±√(4ax)

y = √(4ax) = 2√ax

dy/dx = d/dx (2√ax)

Using the chain rule, we get:

dy/dx = 2(1/2√ax)(a) = a/√ax

Therefore,  

$ds/dx = \sqrt{(1 + (dy/dx)^2)} = \sqrt{(1 + (a/\sqrt{ ax})^2)}$

Simplifying this  expression, we get:

ds/dx = √(1 + a^2/x)

To learn more about differentiation, visit:

https://brainly.in/question/13142910

To learn more about equation, visit:

https://brainly.in/question/24791936

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