Find and simplify the derivative (quotient rule)

• anonymity
In summary, the conversation discusses finding the derivative of a complicated function and simplifying it. The suggested method is to use algebra to manipulate the function into a more manageable form.
anonymity

Homework Statement

find the derivative of (x2 - 3)4/(2x3+1)3

and simplify

The Attempt at a Solution

as far as i could get was 8x(x2-3)3-18x2(2x3+1)2/(2x3+1)6

which is not simplified.

How can you simplify something like this? Is there a systematic way to approach it?

In general, what is the best method to approach really messy derivatives (such as this one, or any other that can be manipulated by algebra)?

Last edited:
Check your calculation: $$u=(x^{2}-3)^{4}$$ and $$v=(2x^{3}+1)^{3}$$, then:
$$\frac{du}{dx}=8x(x^{2}-3)^{3}\quad\frac{dv}{dx}=18x^{2}(2x^{3}+1)^{2}$$
From here the algebra is doable.

Doh. Thanks lol

1. What is the quotient rule for finding derivatives?

The quotient rule is a formula used to find the derivative of a quotient of two functions. It states that the derivative of f(x)/g(x) is equal to (g(x)*f'(x) - f(x)*g'(x)) / (g(x))^2.

2. When should I use the quotient rule to find a derivative?

The quotient rule should be used when you have a function that is in the form of f(x)/g(x), where both f(x) and g(x) are functions of x.

3. How do I simplify the derivative using the quotient rule?

To simplify the derivative using the quotient rule, you will need to apply the formula and then use algebraic techniques to simplify the resulting expression.

4. Can I use the quotient rule for higher order derivatives?

Yes, the quotient rule can be used for higher order derivatives. You will need to apply the rule multiple times, depending on the order of the derivative you are trying to find.

5. Are there any common mistakes to avoid when using the quotient rule?

One common mistake to avoid when using the quotient rule is forgetting to use the chain rule when taking the derivative of the numerator and denominator separately. It is important to remember to apply the chain rule to both parts of the quotient before simplifying the expression.

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