You're correct, the answer is C.
Given any function of the form [tex]y=x^n[/tex], then the derivative of y with respect to x ([tex] \frac{dy}{dx} [/tex]) is written as:
[tex]\frac{dy}{dx}=nx^n^-^1[/tex]
In which [tex]n[/tex] is any constant, this is called the power rule for differentiation.
For this example we have [tex]y= \frac{2}{x^4} [/tex], first lets get rid of the quotient and write the expression in the form [tex]y=x^n[/tex]:
[tex]y= \frac{2}{x^4} =2x^-^4[/tex]
Now we can directly apply the rule stated at the beginning (in which [tex]n=-4[/tex]):
[tex] \frac{dy}{dx}=(2)(-4)x^{-4-1}=-8 x^{-5}= -\frac{8}{x^5} [/tex]
Note that whenever we differentiate a function, we simply "ignore" the constants (we take them out of the derivative).
