Differentiation using the quotient rule

In summary, when using the quotient rule to differentiate, be careful with algebra and take it step by step to avoid mistakes.
  • #1
rikiki
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Homework Statement



Use the quotient rule to differentiate

y=(〖2x〗^4-3x)/(4x-1)

Homework Equations



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

The Attempt at a Solution



Please also find attached attempt as jpeg for clarity, and textbook supplied answer.

dy/dx=([(4x-1).(8x^3-3)]-[〖(2x〗^4-3x).(4)])/((4x-1)^2 )

dy/dx=([(4).(8×3x^(3-1) )]-[(2×4x^(4-1)-3).(4)])/((4x-1)^2 )

dy/dx=((4).(24x^2 )-(8x^3-3).(4))/((4x-1)^2 )

I think i can take out the two 4's in the numerator, apart from this I'm not entirely sure where I've gone wrong. If anyone has any advice to get me back on track that would be great. Thanks.
 

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  • #2
In your first attempt, you had a massive algebra mistake in the numerator of the derivative. The second attempt appears to be OK.
 

FAQ: Differentiation using the quotient rule

1. What is the quotient rule for differentiation?

The quotient rule is a formula used to find the derivative of a function that is the ratio of two other 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 the quotient rule be used?

The quotient rule should be used when the function to be differentiated is in the form of a ratio of two other functions. It is also used when the power rule or product rule cannot be applied.

3. What are the steps to use the quotient rule?

The steps to use the quotient rule are as follows: 1) Identify the quotient function f(x)/g(x), 2) Differentiate the numerator f(x) using the power rule, 3) Differentiate the denominator g(x) using the power rule, 4) Substitute the differentiated values into the quotient rule formula, and 5) Simplify the resulting expression.

4. Can the quotient rule be used to find higher order derivatives?

Yes, the quotient rule can be used to find higher order derivatives. Each time the quotient rule is applied, the resulting function becomes the new quotient function, and the process can be repeated to find second, third, and higher order derivatives.

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

Yes, some common mistakes when using the quotient rule include: not simplifying the resulting expression, forgetting to use the chain rule for the derivative of the numerator and denominator, and forgetting to square the denominator when substituting into the formula.

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