Finding the second derivative of $$f(x)=\frac{6}{7x^4}$$

My solution:

First, I'm going to rewrite our function so I can use the power rule:


Now I'm going to take the first derivative




Now I will find the second derivative






  • 2
    $\begingroup$ This is correct, as any symbolic calculator like Wolfram Alpha would tell you wolframalpha.com/input/… $\endgroup$ Feb 9 '20 at 13:49
  • 2
    $\begingroup$ It's correct, but you want to use one variable ($x$ or $t$) instead of two! $\endgroup$
    – manooooh
    Feb 9 '20 at 14:01
  • 1
    $\begingroup$ I believe the $t$ in the title was a misprint and I've edited to the title to fix it. $\endgroup$
    – Lee Mosher
    Feb 9 '20 at 16:24

There are two possibilities:

  1. You have messed up writing down the problem and it should be $f(\color{red}x)=\frac6{7\color{red}x^4}$; then your solution is completely fine.
  2. You have not messed up writing down the problem and it is in fact $f(\color{red}x)=\frac6{7\color{red}t^4}$; then you solution is wrong as by taking the derivative w.r.t. $x$ any function of a different variable (as $t$) is considered a constant and the second derivative w.r.t. is just $0$.

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