Question

Find the derivative of f(x) = 5/x at x = -1.

Answer 1

Hey Alex,
recall a helpful exponent rule,\[\large\rm \frac{1}{x}=x^{-1}\]

Answer 2

Applying this rule will allow us to use our power rule for differentiation.

Answer 3

So this would be x^-5?

Answer 4

No but good guess.\[\large\rm \frac{5}{x}=5\cdot\frac{1}{x}\]

Answer 5

The 5 can just simply come down in front.
And then you can apply the rule to the x-portion sitting next to it.

Answer 6

Is it -1?

Answer 7

\[\large\rm f(x)=\frac5x\qquad\qquad\qquad\to\qquad\qquad\qquad f(x)=5x^{-1}\]Ok yes, good.
That's how we bring the x up to the numerator,
we apply a -1 power to it.

Now it's ready for power rule.
Remember how to do that?

Answer 8

-1 * 5 = -5?

Answer 9

I don't quite understand.