Mathematics

The key is recognizing this as a quotient rule problem where the numerator involves a composite function. You'll need the chain rule for $\ln(4x^2+1)$ in the numerator, then apply quotient rule: $\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}$. Keep track of each piece carefully—the derivative of the logarithm and the exponential in the denominator will both contribute to the final expression.

The key is recognizing this as a quotient rule problem where the numerator involves a composite function. You'll need the chain rule for $\ln(4x^2+1)$ in the numerator, then apply quotient rule: $\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}$. Keep track of each piece carefully—the derivative of the logarithm and the exponential in the denominator will both contribute to the final expression.