Find dy/dx in terms of x and y

Question

Find dy/dx in terms of x and y if x^9+y^2=√2

dy/dx=_____

Answer 1

I would solve for y, since only one term has a y factor.

 

y² = -x⁹ + √2

 

y = (-x⁹ + √2)^1/2

 

 

Now you derivative y in terms of x explicitly.

Answer 2

9x⁸ + 2yy' = 0

2yy' = -9x⁸

y' = -9x⁸/2y