If y=1/x^2, find dy/dx|x=-2

Question

lukecrayonz · Answer

Just do the deriv and input x=-2?

psymon · Answer

Yep.

lukecrayonz · Answer

1/4 :)

psymon · Answer

Looks good to me.

lukecrayonz · Answer

How would you find the deriv to this?

lukecrayonz · Answer

Without the whole x+h dealio

psymon · Answer

Well, this kind of derivative in particular has a pretty fast way of doing it. The long way would be that you need to make the x^2 into a negative exponent like this:

$$\frac{ 1 }{ x ^{2} }=x ^{-2}   $$
Then you would use the power rule formula for derivatives, which is:
$$x ^{n}\implies nx ^{n-1}   $$So with n being -2, we use the formula to get:
$$-2x ^{-3} =\frac{ -2 }{ x ^{3} }    $$

These fraction derivatives have a pattern tot hem, though, that make them a little easier.

lukecrayonz · Answer

That makes a lot of sense:)

lukecrayonz · Answer

Okay and how about finding a line tangent?

lukecrayonz · Answer

Oh wait a little different.. one sec:O

lukecrayonz · Answer

For the function, find the pts on the graph at which the tangent line is horiziontal. If none exist, state that fact.

psymon · Answer

Well, the derivative is a formula for slope. So if you want the slope at a specific point, you take the derivative then plug in the x-coordinate into the derivative. And tangent line being horizontal means slope = 0. And since the derivative is a formula for slope, you want to find all the pointswhere the derivative = 0.