using the quotient rule to differentiate

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June 26th 2012, 11:27 AM
tomjay

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
June 26th 2012, 11:39 AM
Plato

Re: using the quotient rule to differentiate

Quote:

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)

$\left(\frac{f}{g}\right)'=\frac{f'g-g'f}{g^2}$
June 26th 2012, 11:41 AM
tomjay

Re: using the quotient rule to differentiate

thanks for the quick response any chance you can show your working to help me understand it....
June 26th 2012, 11:52 AM
Plato

Re: using the quotient rule to differentiate

Quote:

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.
June 26th 2012, 11:56 AM
tomjay

Re: using the quotient rule to differentiate

thanks for that think I need more time with the work books
June 26th 2012, 12:37 PM
tom@ballooncalculus

Re: using the quotient rule to differentiate

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

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

Just in case a picture helps...

http://www.ballooncalculus.org/draw/diffProd/eleven.png

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

Spoiler:

http://www.ballooncalculus.org/asy/chain.png

... 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...

http://www.ballooncalculus.org/asy/prod.png

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

The general drift is...

http://www.ballooncalculus.org/asy/maps/diffQuot.png

The rest...

Spoiler:

http://www.ballooncalculus.org/draw/...od/elevena.png

Simplify the bottom row.

__________________________________________________ _________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!
June 26th 2012, 01:46 PM
HallsofIvy

Re: using the quotient rule to differentiate

Quote:

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 $f(x)= 2x^4- 3x$ and the denominator is $g(x)= 4x- 1$ . What is f'(x)? What is f'g? What is g'(x)? What is fg'? What is $g^2$ ?