Question

Find the derivative y' of the function:
y=(x/(x^2+1))^4

Answer 1

oh boy chain rule, quotient rule, power rule..

Answer 2

is this implicit differentiation?

Answer 3

no, you just have y on its own on the left. No need for that.

Answer 4

\[y=\frac{x^4}{(x^2+1)^4}\]
\[y'=\frac{(x^2+1)^4(4x^3)-(x^4)(4(x^2+1)^3(2x)}{(x^2+1)^8}\]

Answer 5

You probably want to clean that up a little.

Answer 6

wow it's that long...

Answer 7

it will clean up a lot!

Answer 8

No doubt.

Answer 9

you could also use
\[f'(x)=4\left(\frac{x}{x^2+1}\right)^3\times \frac{d}{dx}\left(\frac{x}{x^2+1}\right)\] but there is no avoiding the quotient rule somewhere

Answer 10

just might be neater in the end use the chain rule. second term is
\[\frac{-x^2+1}{(x^2+1)^2}\] so maybe less algebra at the end