Question

What is the derivative of y with respect to x if y = 2/X4

Answer 1

You're correct, the answer is C.

Given any function of the form $y=x^n$, then the derivative of y with respect to x ($\frac{dy}{dx}$) is written as:
$\frac{dy}{dx}=nx^n^-^1$

In which $n$ is any constant, this is called the power rule for differentiation.

For this example we have $y= \frac{2}{x^4}$, first lets get rid of the quotient and write the expression in the form $y=x^n$:
$y= \frac{2}{x^4} =2x^-^4$

Now we can directly apply the rule stated at the beginning (in which $n=-4$):
$\frac{dy}{dx}=(2)(-4)x^{-4-1}=-8 x^{-5}= -\frac{8}{x^5}$

Note that whenever we differentiate a function, we simply "ignore" the constants (we take them out of the derivative).