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

• Ris Valdez
In summary,The student attempted to solve a homework problem involving the quotient rule, but did not correctly use brackets. Wiley marked the answer incorrect because it did not use the correct format.
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.

Ris Valdez said:

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.

PeroK said:
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?

Ris Valdez said:
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?

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).

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.

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:

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

What is Calculus?

Calculus is a branch of mathematics that deals with the study of change and continuous processes. It is divided into two main branches: differential calculus, which focuses on the rate of change of quantities, and integral calculus, which deals with the accumulation of quantities.

What are limits in Calculus?

Limits in Calculus are used to describe the behavior of a function as the input approaches a certain value. It is essentially the value that a function is approaching, rather than the actual value at that point.

How do I find f'(x)?

To find f'(x), also known as the derivative of a function, you can use the power rule, product rule, quotient rule, or chain rule. These are different methods used to find the rate of change of a function at a specific point.

There can be several reasons why your answer may be wrong when finding f'(x). Some common mistakes include not applying the correct derivative rule, miscalculations, or not simplifying the expression correctly. It is important to double check your work and make sure you are following the correct steps.

Can I use a calculator to find f'(x)?

Yes, you can use a calculator to find f'(x). However, it is important to understand the concepts and rules behind finding derivatives by hand before relying on a calculator. Additionally, some calculators may not give the most simplified form of the derivative, so it is important to check your answer manually as well.

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