Find dy/dx in terms of x and y

Question

Find dy/dx in terms of x and y

if ⁵√x= 4√y

then dy/dx is? 

Answer 1

5√x = 4√y
I see probably two answers, one is if 4 and 5 are coefficients:
√y =(5/4)√x.
squaring the two sides we obtain:
y = (25/16) x
dy/dx = (25/16)
The other occurs if the equation is:
X^(1/5) = Y^(1/4)
elevating both sides to the 4 power we get:
X6=^(4/5) = Y
dy/dx = (4/5) Y^(-1/5)
I think I solved the two possibilities of this problem

Answer 2

I assume the problem is:

 

x^1/5 = y^1/4

 

Raise both sides of the equation to the 4th power:

 

(x^1/5)⁴ = (y^1/4)⁴

 

x^4/5 = y

 

To find dy/dx, use the power rule:

 

dy/dx = (4/5)*x^-1/5