Calculus: Limits Homework - Find f'(x) & Why Wrong?

[Ris Valdez]

Homework Statement

Find f ' (x) if f(x) = 4x + 4 / x² + 4

Homework Equations

I used the mnemonic "lo dhi - hidlo / (lo)^2

The Attempt at a Solution

I got -4x^2 +16-8x / (x^2+4)^2
but it's telling me I'm wrong? Why? I computed it again but I still got the same answer.

 

[PeroK]

Homework Statement

Find f ' (x) if f(x) = 4x + 4 / x² + 4

Homework Equations

I used the mnemonic "lo dhi - hidlo / (lo)^2

The Attempt at a Solution

I got -4x^2 +16-8x / (x^2+4)^2
but it's telling me I'm wrong? Why? I computed it again but I still got the same answer.

If you're doing calculus, you need to be able to write your expressions correctly. Please put brackets where they are required. It's impossible to know what expressions you are actually dealing with here.

 

[Ris Valdez]

If you're doing calculus, you need to be able to write your expressions correctly. Please put brackets where they are required. It's impossible to know what expressions you are actually dealing with here.

Sorry!

Problem: find f ' (x) if f(x) = (4x + 4) / (x^2 + 4)

My answer (which was marked wrong by wiley): (-4x^2 + 16 - 8x) / [(x^2 + 4) ^2]

Is that good enough?

 

[PeroK]

Sorry!

Problem: find f ' (x) if f(x) = (4x + 4) / (x^2 + 4)

My answer (which was marked wrong by wiley): (-4x^2 + 16 - 8x) / [(x^2 + 4) ^2]

Is that good enough?

Your answer looks correct to me.

 

[verty]

At first I got a different answer, it was because I didn't put brackets around the second term. It's quite easy to make that mistake, so I'll bet Wiley wanted the 8x to be positive (which wouldn't be correct).

 

[HallsofIvy]

Who is this "Wiley" person and how did he or she mark your answer incorrect? If you are using some "mechanical" scoring, those things are notorious for marking wrong anything that is not in exactly the form it wants.

 

[STEMucator]

The quotient rule is quite ugly to use in general (which is what you have used to find the answer).

It is actually much easier to re-write the expression as:

$$f(x) = \frac{4x + 4}{x^2 + 4} = (4x + 4)(x^2 + 4)^{-1}$$

This allows you to take advantage of the product and chain rules, and usually you will be able to find the derivatives of quotients much faster:

$$f(x) = \frac{4x + 4}{x^2 + 4} = (4x + 4)(x^2 + 4)^{-1} = (4)(x^2 + 4)^{-1} - (4x + 4)(x^2 + 4)^{-2}(2x)$$