differentiate x^ln(2x^2+3) wrt x.
Let u = ln(2x^2 + 3), and y = x^u
For y = x^u, take logs of both sides, giving
ln(y) = u.ln(x)
now differentiate both sides wrt x.
(1/y)y' = u'.ln(x) + u/x and u' = du/dx = 4x/(2x^2+3)
y' = y{[4x/(2x^2+3)].ln(x) + ln(2x^2+3)/x}
y' = x^ln(2x^2+3){4x.ln(x)/(2x^2+3) + ln(2x^2+3)/x}