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

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

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

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

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

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

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

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

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 $$0$$.