Question

Finding a Second Derivative In Exercises 91, 92, 93, 94, 95, 96, 97, 98, 99, and 100, find the second derivative of the function.

Answer 1

Given:

`f(x)=x^2+3x^(-3)`

The first derivative is:

`\begin{gathered} f^(\prime)(x)=2x^(2-1)+3\cdot(-3)x^(-3-1) \\ Simplify \\ f^(\prime)(x)=2x-9x^(-4) \end{gathered}`

And the second derivative is:

`f^(\prime)^(\prime)(x)=2x^(1-1)-9(-4)x^(-4-1)=2(1)+36x^(-5)=2+36x^(-5)`

Answer:

`\begin{equation*} 2+36x^(-5) \end{equation*}`