Answer:
A general rule for functions of the general form:
y = A*x^n
is:
dy/dx = n*A*x^(n - 1)
Then, for the function:
y^2 = 4*a*x
Then we can rewrite this as:
y = (4*a*x)^(1/2) = √(4*a)*x^(1/2)
Then we have:
A = √(4*a)
n = 1/2
Now we can use the above rule to get
dy/dx = (1/2)*√(4*a)*x^(1/2 - 1)
dy/dx = (1/2)*√(4*a)*x^(-1/2)
dy/dx = (1/2)*√(4*a/x)
dy/dx = √(1/4)*√(4*a/x)
dy/dx = √( (1/4)*4*a/x)
dy/dx = √(a/x)
