Use logarithmic differentiation to find the derivative. y=\sqrt[4]{(x^2+9)/(x^2+10)} y'=?

Answer 1

f(x) = [(x²+9)/(x²+10)]^1/4

f'(x)

= f(x) {ln(f)}'

= [(x²+9)/(x²+10)]^1/4 { (1/4) [ln(x²+9) - ln(x²+10)] }'

= [(x²+9)/(x²+10)]^1/4 (1/4) [2x/(x²+9) - 2x/(x²+10)]