Question

Question #3c6fa

Answer 1

`d/dy[1/y]=-1/y^2`

Explanation:

First rewrite the derivative as `d/dy[y^-1]`. This makes it easy to use the power rule.

The power rule states that `d/dx[x^n]=nx^(n-1)` where `n` is a constant.

Applying the power rule, we get `d/dy[y^-1]=-1*y^(-1-1)=-y^-2`

Which we can rewrite as `-1/y^2`

Note: if you're being asked to take that derivative with respect to `x` (i.e. `d/dx[1/y]`), you will need to use implicit differentiation. The only extra step, however, is to tag on a `dy/dx` to the end of that expression.

Your final answer would then be `-1/y^2 [dy/dx]`