Question

\(\Huge \frac {d (\frac {4^x}{1+x^3})}{dx}\)=?

Answer 1

use the quotient rule
(4^x) ' = ln4 *4^x

Answer 2

let
\[\Large y=\frac{4^x}{1+x^3}\]
take natural log of both sides
\[\Large \ln (y)=\ln(\frac{4^x}{1+x^3})\]
or
\[\Large \ln(y)=\ln(4^x)-\ln(1+x^3)\]
\[\Large \ln(y)=x*\ln(4)-\ln(1+x^3)\]
just differentiate both sides with respect to x

Answer 3

what i've done is
\(\Huge \frac {(4^x)[(1+x^3)ln 4 -3x^2]}{(1+x^3)^2}\)
can it be more simplified? or I've wrong?

Answer 4

nope that's fine.

Answer 5

ok thanks.