Question

How do you implicitly differentiate `1=x^3y + 5xy`?

Answer 1

`dy/dx=-(3x^2y+5y)/(x^3+5x)`

Explanation:

Use the product rule in both terms on the right hand side.

Recall that implicitly differentiating a `y` term will create a `dy/dx` term.

`0=3x^2y+x^3dy/dx+5y+5xdy/dx`

Isolate the `dy/dx` terms to solve for them.

`-3x^2y-5y=dy/dx(x^3+5x)`

`dy/dx=-(3x^2y+5y)/(x^3+5x)`