# Thread: using the quotient rule to differentiate

1. ## using the quotient rule to differentiate

getting myself into panic stations at the thought of calculus.....

how would I differentiate using the quotent rule with respect to x for

y = (2x4 - 3x) / (4x - 1)

thanks for any help given

2. ## Re: using the quotient rule to differentiate

Originally Posted by tomjay
getting myself into panic stations at the thought of calculus.....

how would I differentiate using the quotent rule with respect to x for

y = (2x4 - 3x) / (4x - 1)
$\displaystyle \left(\frac{f}{g}\right)'=\frac{f'g-g'f}{g^2}$

3. ## Re: using the quotient rule to differentiate

thanks for the quick response any chance you can show your working to help me understand it....

4. ## Re: using the quotient rule to differentiate

Originally Posted by tomjay
thanks for the quick response any chance you can show your working to help me understand it....
There are no workings to it. That is the quotient rule.
The derivative of the numerator times the denominator minus the derivative of the denominator times numerator all divided by the denominator squared.

5. ## Re: using the quotient rule to differentiate

thanks for that think I need more time with the work books

6. ## Re: using the quotient rule to differentiate

Many people prefer to treat the quotient as a product...

$\displaystyle \frac{f}{g} = f\ g^{-1}$

Just in case a picture helps...

... where (key in spoiler) ...

Spoiler:

... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

But this is wrapped inside the legs-uncrossed version of...

... the product rule, where, again, straight continuous lines are differentiating downwards with respect to x.

The general drift is...

The rest...

Spoiler:

Simplify the bottom row.

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7. ## Re: using the quotient rule to differentiate

Originally Posted by tomjay
thanks for that think I need more time with the work books
Could you at least try to do it yourself? In your example, the numerator is $\displaystyle f(x)= 2x^4- 3x$ and the denominator is $\displaystyle g(x)= 4x- 1$. What is f'(x)? What is f'g? What is g'(x)? What is fg'? What is $\displaystyle g^2$?