find dy/dx in terms of x and y

Question

Find dy/dx in terms of x and y if ^4√x=3√y.

dy/dx=_____

Answer 1

You can also rewrite the equation using rational exponents.

 

x^1/4 = 3y^1/2

 

 

Use implicit differentiation using the chain-rule.

 

(1/4)x^-3/4 = (3/2)y^-1/2y'

 

 

Multiply both sides of the equation by (2/3)y^1/2 of y'.

 

(1/4)x^-3/4 * (2/3)y^1/2 = y'

 

√y / (6 * ⁴√(x³)) = y'

Answer 2

Let's simplify: ⁴√x=3√y => √y or y^½ = x^¼ / 3

 

Let's square both sides. So, y = x^½ / 9

 

dy/dx = ½ * (1/9) x ^-½ = 1 / (18√x)