Implicit Differentiation

Find \(\,\dfrac{dy}{dx}\,\) by implicit differentiation.

1. \(\sqrt{x}-3\sqrt{y}=5 \)  solution

2. \(\displaystyle{ 2x^3-6y^3=8 } \)  solution

3. \(\displaystyle{\frac{1}{x^3} + \frac{1}{y^2}=2 }\)  solution

4. \(\displaystyle{5x^3+3y =5-3x+4y^2 }\)  solution

5. \(\displaystyle{x y - y^3 = 4x-1} \)  solution

6. \(\displaystyle{ x^2-xy+y^2= 5} \)   solution