derivitives?

Question

How do u take the derivitive of 8/x^2+4?

Answer 1

Assume
y = f(x) = 8 / (x² + 4)------(which is NOT what you have posted)
Method 1
let u = x² + 4
du/dx = 2x
y = 8 / u
y = 8.u^(-1)
dy/du = - 8 u^(-2) = - 8 / u² = - 8 / (x² + 4)²
dy/dx = (dy/du).(du/dx)
dy/dx = (-16x) / (x² + 4)²

Method 2
f(x) = 8.(x² + 4)^(-1)
f `(x) = (-8).(2x)(x² + 4)^(-2)
f `(x) = (-16x) / (x² + 4)²

PS: Remember brackets when submitting questions as these give the question a completely different meaning. Lack of brackets leads to incorrect answers and time being wasted.
Cheers!

Answer 2

The derivative of ax^(n)+b is:
nax^(n-1). So your derivative is found by:
n= -2
a=8
b=4
giving: derivative of 8/x^2+4
think of 8/x^2 as 8*(x^(-2))
= -2*8x^-3
= -16/x^3 or -16*x^-3
The 4 goes away because it is not the coefficient of any x.


Ah yes, well, if it is 8/((x^2)+4) that is a little more difficult...
Which through some work with the chain rule I seem to have gotten
(8/((x^2)+4)) - (16/((x^5)+4x^3)) Which just looks wrong...

Answer 3

The derivative if 2x^2 is 4x...so to apply the same concept you need to make a little change.

8
----
X^2 can be written as 8X^(-2)...therefore the derivative should be -16x^(-3)
or -16
-----
X^3
The derivative of any constant is always 0 so the final answer is...
-16
-----
X^3

Answer 4

Do you know the quotient rule, probably not, assuming you mean 8/(x^2+4), the derivative would be (-8(2x))/((x^2+4)^2). If you mean (8/(x^2))+4, the derivative would be (-8(2x)/(x^4). You need to remember your rules.