Derivative of

Question

log base 4( x^2+1)=y?

Answer 1

log₄ (x²+1) = y

Rewrite the expression 

log (x²+1) / log (4) = y                                      [ Log_a^x  = log x / log a  ]

Now apply derivative with respect to x .

y ' = [ [ 1/ (x²+1) ] / log (4) ] (x²+1)' 

y ' =  [ 1/ (x²+1) * log (4) ] (2x) 

y ' =  2x / (x²+1) * 0.6020

y ' =  3.32x / (x²+1) 

So the derivative of the function is y ' =  3.32x / (x²+1)