0
$\begingroup$

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:

$f(x)=\frac{6}{7x^4}=\frac{6}{7}x^{-4}$

Now I'm going to take the first derivative

$f'(x)=\frac{6}{7}\frac{d}{dx}x^{-4}$

$f'(x)=\frac{6}{7}(-4)x^{-5}$

$f'(x)=\frac{-24}{7}x^{-5}$

Now I will find the second derivative

$f''(x)=\frac{d}{dx}\frac{-24}{7}x^{-5}$

$f''(x)=\frac{-24}{7}\frac{d}{dx}x^{-5}$

$f''(x)=\frac{-24}{7}(-5)x^{-6}$

$f''(x)=\frac{120}{7}x^{-6}$

$f''(x)=\frac{120}{7x^6}$

$\endgroup$
3
  • 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
2
$\begingroup$

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 $0$.
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.