Question

Differentiate.
y = t^2 + 4/(t^4 − 2t^2 + 1)

Answer 1

\[\Large y\quad=\quad \frac{t^2+4}{t^4-2t^2+1}\]Hmm I guess we could use the quotient rule, yes? :)

Answer 2

\[\large y'\quad=\quad \frac{\color{royalblue}{(t^2+4)'}(t^4-2t^2+1)-(t^2+4)\color{royalblue}{(t^4-2t^2+1)'}}{(t^4-2t^2+1)}\]
Understand the setup? We need to take the derivative of the blue parts.

Answer 3

\[y′=((t^{2}+4)′(t^{4}−2t ^{2}+1)−(t ^{2}+4)(t ^{4}−2t ^{2}+1)′)/(t ^{4}-2t ^{2}+1)^{2}\]

Answer 4

Woops my denominator :3

Answer 5

forgot the square