( ( e^( -2( X^(1/2) ) ) / x^(1/2) ) - (dx/dy) = 1
To solve the given equation:
( ( e^( -2( X^(1/2) ) ) / x^(1/2) ) - (dx/dy) = 1
we need to isolate the derivative term (dx/dy) and solve for it.
Step 1: Multiply through by x^(1/2) to remove the fraction:
e^(-2√x) - (dx/dy)(x^(1/2)) = x^(1/2)
Step 2: Add (dx/dy)(x^(1/2)) to both sides to isolate the derivative term:
e^(-2√x) = (dx/dy)(x^(1/2)) + x^(1/2)
Step 3: Factor out (dx/dy) on the right side:
e^(-2√x) = (dx/dy)(x^(1/2) + 1)
Step 4: Divide both sides by (x^(1/2) + 1) to solve for (dx/dy):
(dx/dy) = e^(-2√x) / (x^(1/2) + 1)
Therefore, the solution for the derivative term (dx/dy) is:
(dx/dy) = e^(-2√x) / (x^(1/2) + 1)