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

Question

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

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

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

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

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

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

Answer 1

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 $0$.