Given f(x)=(x2+1)xf(x) = (x^2+1)^xf(x)=(x2+1)x, find f′(x)f'(x)f′(x) using logarithmic differentiation.
(x^2+1)^x \cdot [\ln(x^2+1) + \frac{2x^2}{x^2+1}]
x(x^2+1)^{x-1} \cdot 2x
(x^2+1)^x \cdot \ln(x^2+1)
x(x^2+1)^{x-1}