Question

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

A. 8/X5
B. 8/X3
C. -8/X5 <---I think it's this one. Not sure.
D. -8/X3

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 (
`(dy)/(dx)`) is written as:

`(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= (2)/(x^4)`, first lets get rid of the quotient and write the expression in the form
`y=x^n`:

`y= (2)/(x^4) =2x^-^4`

Now we can directly apply the rule stated at the beginning (in which
`n=-4`):

`(dy)/(dx)=(2)(-4)x^(-4-1)=-8 x^(-5)= -(8)/(x^5)`

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