Question

How do you implicitly differentiate `3x^2-y^2=7`?

Answer 1

`dy/dx=(3x)/y`

Explanation:

When we implicitly differentiate with respect to `x`, we differentiate the `x` terms like we normally would. However, when we reach a variable that's not `x` (in this case, `y`), the chain rule kicks into effect and a `dy/dx` term is spit out.

`d/dx[3x^2-y^2=7]`

`6x-2ydy/dx=0`

`-2ydy/dx=-6x`

`dy/dx=(3x)/y`