what is the derivative of this function?

Question

f(x) = 1/4 ln (x^4)/ (1+x^4)

Answer 1

use the property of natural logarithm...

f(x) = (1/4) [4lnx - ln(1+x^4)]
= lnx - (1/4) ln(1+x^4)

thus
f'(x) = 1/x - (1/4)(1/(1+x^4))*(4x^3)
= 1/x - (x^3/(1+x^4))


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Answer 2

f (x) = ln x / (1 + x^4)
Using quotient rule:-
f `(x) = [(1 + x^4)(1 / x) - (ln x)(4x³)] / (1 + x^4)²