What is the second derivative of #f(x)= 8/x-2#?

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Answer 1 · 2015-12-10T17:11:49

#16/(x^3)#

The first derivative is:
#d/(dx)8/x - d/(dx)2#

Rewriting,
#d/(dx)8*x^-1 - d/(dx)2#

Using derivative rules, and the fact that the derivative of any constant is zero,
#8*d/(dx)x^-1 - 0#

Using the power rule to finish,
#-8*x^-2#

This is our first derivative. To find the second, we simply take the derivative of the above expression:
#d/(dx)-8x^-2#

All we need to do is use the power rule again:
#16x^-3#

In another form:
#16/(x^3)#

And we're done.