Solving Derivative of 6x/(x2+3)2

[phillyolly]

Homework Statement

6x/(x²+3)²

The Attempt at a Solution

If I solve this function as a multiplication, i.e.

6x (x²+3)^-2

my answer is

f ' (x)=[ (x-3)(x-1) ]/(x²+3)³

If I solve it as a fraction
f ' (x)=(v'g-g'v)/g²

I get

f ' (x)=(x²-1)/(x²+3)³


This is all so confusing. Please help me out. Thank you.

 

[vela]

Neither is correct. Show us your steps so we can see where your mistakes lie.

 

[michonamona]

6x (x²+3)^-2


Did you use the product rule followed by the chain rule?

You can consider this function as:

h(x)=f(x)g(p(x))

where:

f(x)=6x, g(z) = z^-2 ,and p(x)=x²+3

Now how would you take the derivative of h(x)?

Hint: h'(x)=f'(x)g(p(x))+f(x)g'(p(x))p'(x)