Find the derivative of f(x) = -8/x at x = 11.

Question

anonymous · Answer

by hand or using a shortcut?

kainui · Answer

You can rewrite $$\frac{1}{x} =x^{-1}$$
this is just a consequence of exponent rules lining up. Since $$x^3*x^2=(x*x*x)(x*x)=x^5$$ we know exponents add. So if you have $$\frac{x^5}{x}=x^4 $$ then we could just as well write this as $$x^5*x^{-1}=x^4$$ by following these same rules...

But the whole point of understanding that is just because the power rule works just the same here as well. $$\frac{d}{dx}(x^p)=p*x^{p-1}$$

anonymous · Answer

if you get to use a shortcut, then 
$$\frac{d}{dx}[\frac{1}{x}]=-\frac{1}{x^2}$$

kainui · Answer

I just assumed you weren't using the limit definition, @satellite73 has a good point.

anonymous · Answer

if you have to compute a limit by hand, then the work is different

kainui · Answer

Although not a good point in his second post where he just gives you the answer for free with no explanation.

anonymous · Answer

8/121?