Implicit Derivative

Question

Find dy/dx, where 4x^2+10y^2−3=0.

dy/dx=

Answer 1

Implicitly differentiate 4x² + 10y² − 3 = 0 to 8x + 20yy' − 0 = 0.

Then rewrite as 20yy' = -8x or 5yy' = -2x or y' = -2x/5y.

4x² + 10y² − 3 = 0 gives y = ±(0.3 − 0.4x²)^0.5.

Then y' = -2x/5y becomes y' = -2x/±5(0.3 − 0.4x²)^0.5

or y' = ±0.4x/(0.3 − 0.4x²)^0.5.

Rearranging 4x² + 10y² − 3 = 0 as 10y² = 3 − 4x² and then as y = ±(0.3 − 0.4x²)^0.5 will also

lead to dy/dx = ±(0.5)(-0.8x)(0.3 − 0.4x²)^-0.5 or y' = ±0.4x/(0.3 − 0.4x²)^0.5 as above.

Answer 2

4x² + 10y² - 3 = 0

8x + 20y(dy/dx) = 0

20y(dy/dx) = -8x

dy/dx = -2x / (5y)