Question

If `f(x)=x^(-5/7)`, how do you compute f'(3)?

Answer 1

`~~-0.109`

Explanation:

Here, we can use the Power Rule

`d/dx(x^a)=ax^(a-1)`

If this looks foreign to you, it's really straightforward:

• The constant comes out front
• The exponent is decremented by `1`

Doing this, we get

`-5/7x^(-5/7-7/7)`

`=>f'(x)=-5/7x^(-12/7)`

Now, we can plug in `3` for `x` to evaluate `f'(3)`. We get

`f'(3)=-5/7(3)^(-12/7)`

`=>-5/7*(1/3^(12/7))`

which is approximately equal to `-0.109`

Notice, we only used the Power Rule here, stated above, and we evaluated the expression at `3`.

Hope this helps!