logarithmic differentiation: f(x) = (x^2 + 1)^(x + 1)

[lbaird]

Having a problem trying to solve the derivative for the following:
f(x)=(x^2+1)^(x+1) hint: use logarithmic differentiation.

I began with ln f(x)=(x+1) ln (x^2+1) but I'm not really sure what to do next.

Thanks!

 

[stapel]

How far have you gotten in the log-diff process? You've replaced "f(x)" with "y", you've logged both sides and differentiated the results with respect to "x", and... then what?

Please be specific. Thank you.

Eliz.

 

[skeeter]

Having a problem trying to solve the derivative for the following:
f(x)=(x^2+1)^(x+1) hint: use logarithmic differentiation.

I began with ln f(x)=(x+1) ln (x^2+1) but I'm not really sure what to do next.

Thanks!

y = (x^2 + 1)^(x + 1)

lny = (x + 1)ln(x^2 + 1)

take the derivative of both sides ...

y'/y = (x + 1)[2x/(x^2 + 1)] + ln(x^2 + 1)

y' = y[(x + 1)[2x/(x^2 + 1)] + ln(x^2 + 1)]

y' = [(x + 1)[2x/(x^2 + 1)] + ln(x^2 + 1)](x^2 + 1)^(x + 1)