Brief calculus.

Question

Use implicit Differentiation to find dy/dx.

3x²-5y⁷ = 10

Answer 1

3x²-5y⁷ = 10

-5y⁷ = 10-3x²

divide both sides by -5

y⁷ = (3x²-10)/5

Get the seven root of both sides:

y = ((3x²-10)/5)^1/7

Differentiate both sides of the original equation with respect to x.

6x - 35y⁶ (dy/dx) = 0

- 35y⁶ (dy/dx) = - 6x

dy/dx = 6x/ (35((3x²-10)/5)^6/7) or (6/35)x/((3x²-10)/5)^6/7