Learn Math Questions

from a handpicked tutor in LIVE 1-to-1 classes

from a handpicked tutor in LIVE 1-to-1 classes

# Find y'' by implicit differentiation. x^{2} + 7y^{2} = 7

**Solution:**

Given x^{2} + 7y^{2} = 7

Using __implicit differentiation__,

2x. dx/dx + 7 2ydy/dx = 0

2x + 14y dy/dx = 0

From further differentiation, we get

2 +14(dy/dx. dy/dx + y.d²y/dx²) = 0

2+ 14((dy/dx)² + y. d²y/dx²) = 0

14((dy/dx)² + y. d²y/dx²) = -2

((dy/dx)² + y. d²y/dx²) = -1/7

(y. d²y/dx²) = -1/7 - (dy/dx)²

d²y/dx² = [-1/7 - (dy/dx)²] / y

Hence y'' = [-1/7 - (dy/dx)²] / y

## Find y'' by implicit differentiation. x^{2} + 7y^{2} = 7

**Summary:**

y'' by implicit differentiation of x^{2} + 7y^{2} = 7 is [-1/7 - (dy/dx)²] / y

Math worksheets and

visual curriculum

visual curriculum