f(x)= (1+x^2)^tanxlnf(x) = (tanx)ln(1+x^2)f'(x)/f(x)= (secx)^2.ln(1+x^2) + 2x.tanx/(1+x^2)f'(x) = [(secx)^2.ln(1+x^2) + 2x.tanx/(1+x^2)] . (1+x^2)^tanx