Question

My question is finding the derivitive of
y=((x+λ)^4)/(x^4+λ^4).
I distributed the exponent in the numerator, but I don't know if that's right. Rewritten as y=(x^4+λ^4)/(x^4+λ^4).
I found the derivitive and multiplied accordingly, as
((4x^3+4λ^3)(x^4+λ^4)-(4x^3+4λ^3)(x^4+λ^4))/(x^4+λ^4)^2. I got
y=4x^7+4x^3λ^4+4λ^3x^4+4λ^7-4x^7-4x^3λ^4-4λ^7.
All of the numerator just winds up canceling out and I don't think that's right.

Answer 1

y=(x+λ)^4/(x^4+λ^4)

y' =

4(x+λ)^3(x^4+λ^4) - (x+λ)^4(4x^3)
-----------------------------------------
(x^4+λ^4)^2

=
(4λ)(λ+x)^3(λ^3-x^3)
--------------------------
(x^4+λ^4)^2

Answer 2

(a+b)^4 is NOT a^4+b^4