Differentiation quotient rule question, am i wrong or is my book wrong?

In summary, the differentiation quotient rule is a formula used in calculus to find the derivative of a quotient of two functions. It is used by multiplying the bottom function by the derivative of the top function, subtracting the top function multiplied by the derivative of the bottom function, and then dividing by the square of the bottom function. To use this rule correctly, make sure to follow the formula and check for algebraic errors. This rule is best used when the functions are too complex for other differentiation rules. If your answer does not match the book's, double check your calculations and simplify your answer. This rule can be applied to any quotient of functions as long as they are differentiable, but it may not always be the most efficient method.
  • #1
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Differentiate with respect to x; (using the quotient rule)
3/2x-1 (3 over 2x minus 1)
dy/dx = (2x-1)(0) - (3)(2) / (2x-1)^2
dy/dx = -6/(2x-1)^2

but my book gives -2/(2x-1)^2

now,
y = u/v and i take
u = 3 and
v = 2x-1.

dy/dx = v(du/dx) - u(dv/dx) / (v)^2

hmm...
 
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  • #2
Assuming the question is to find

[tex]\frac{d}{dx} \; \frac{3}{2x-1} [/tex]

then your answer is correct. Whoever wrote the solutions probably forgot all about the 3.

--Elucidus
 
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1. What is the differentiation quotient rule?

The differentiation quotient rule is a formula used in calculus to find the derivative of a quotient of two functions. It states that the derivative of a quotient is equal to the bottom function times the derivative of the top function, minus the top function times the derivative of the bottom function, all divided by the square of the bottom function.

2. How do I know if I am using the differentiation quotient rule correctly?

To use the differentiation quotient rule correctly, make sure you are following the correct formula and applying it to the correct functions. Also, double check your algebra to ensure that your final answer is in the correct form.

3. When should I use the differentiation quotient rule?

The differentiation quotient rule is used when you need to find the derivative of a quotient of two functions. This can be helpful when the functions are too complex to use other differentiation rules, such as the power rule or product rule.

4. What should I do if my answer using the differentiation quotient rule does not match the answer in my book?

If your answer does not match the answer in your book, it could be due to a mistake in your calculations or a different form of the answer. Double check your work and try simplifying your answer to see if it matches the one in your book.

5. Can the differentiation quotient rule be applied to any quotient of functions?

Yes, the differentiation quotient rule can be applied to any quotient of functions, as long as the functions are differentiable. However, it may not always be the most efficient method for finding the derivative, so it is important to consider other rules as well.

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