Question

What is the second derivative of `x^2 + (16/x)`?

Answer 1

`:. d^2/dx^2( x^2 + 16/x) = 2 +32/x^3`

Explanation:

You should learn the power rule for differentiation, which is that:
`d/dx(x^n) = nx^(n-1) AA n in RR`

So, `d/dx( x^2 + 16/x) = d/dx (x^2 + 16x^-1)`
`:. d/dx( x^2 + 16/x) = 2x^(2-1) + 16(-1)x^(-1-1)`
`:. d/dx( x^2 + 16/x) = 2x -16x^-2`

And differentiating a second time, gives us:
`d^2/dx^2( x^2 + 16/x) = 2(1)x^(1-0) -16(-2)x^(-2-1)`
`:. d^2/dx^2( x^2 + 16/x) = 2x^0 +32x^-3`
`:. d^2/dx^2( x^2 + 16/x) = 2 +32/x^3`