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I have the problem: Find the Derivative: $$\frac{4y^6-6y}{e^{4y}+y}$$

I used the quotient rule $$ \left( \frac{f}{g}\right)' = \frac{f'g-fg'}{g^2}$$

After deriving, I got $$\frac{(24y^5-6)(e^{4y}+y)-(4y^6-6y)(4e^{4y}+1)}{(e^{4y}+y)^2}$$

Do I need to use the chain rule on $g^2$ before simplifying? What about $g$ in the top equation?

Rumplestillskin
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ASTR
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    It looks like you've applied the quotient rule correctly. Only thing left to do is to check for any simplification, common factors. – sharding4 Jun 15 '17 at 03:06

3 Answers3

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that depends on what does $\left(\frac{f}{g} \right)'$ refers to.

No if $\left(\frac{f}{g} \right)'=\frac{d}{dy}\left( \frac{f}{g}\right).$

Yes if $\left(\frac{f}{g} \right)'=\frac{d}{dx}\left( \frac{f}{g}\right).$

Siong Thye Goh
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No, you don't need to perform chain rule on $g^2$.

Glorfindel
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Akshat Jha
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Chain rule is used when you're finding the derivative, since there is no derivative applied to $g^2$ it makes no sense to apply the chain rule.

kingW3
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