Question

How do you find the derivative of `xy^2`?

Answer 1

If you want to differentiate this expression as part of an implicit differentiation problem, here is how:

Explanation:

Assuming that we want to find the derivative with respect to `x` of `xy^2` (assumong that `y` is a function of `x`:

First use the product rule:

`d/dx(xy^2) = d/dx(x) y^2 + x d/dx(y^2)`

Now for `d/dx(y^2)` we'll need the power and chain rules.

`d/dx(xy^2) = 1 y^2 + x [2y dy/dx]`

`d/dx(xy^2)= y^2 +2xy dy/dx`

If you want to differentiate the expression with respect to `t` then the derivatives above are all `d/dt` and `(dx)/dt` may not be `1`.

`d/dt(xy^2) = y^2dx/dt + 2xy dy/dt`

If you want the partial derivatives of the function `f(x,y) = xy^2` that has been answered in another answer.