Question

What is the implicit derivative of `3=1/y -x^2`?

Answer 1

`dy/dx = -2xy^2` The trick is in finding the derivative of each term, for term containing `y` find derivative as usual and put `dy/dx` next to it to indicate it is differentiated with respect to `x`

Explanation:

`3 = 1/y - x^2`

`3 = y^-1 - x^2`

Differentiate both sides with respect to `x`

`d/dx(3) = d/dx(y^-1) - d/dx(x^2)`

`0 = -y^(-1-1)dy/dx - 2x`

`0=-y^-2dy/dx -2x`

`0= -1/y^2 dy/dx -2x`

Add 2x to both the sides

`2x = -1/y^2 dy/dx`

Multiply both sides by `-y^2`

`-2xy^2 = dy/dx`

Answer `dy/dx = -2xy^2`