(1 point) Find $d y / d x$ using the method of logarithmic differentiation when $y=\left(5+9 x^{2}\right)^{\ln (x)}$. \[ d y / d x= \]

Step 1 ：Let \( y = (5 + 9x^2)^{\ln(x)} \)

Step 2 ：Take the natural logarithm of both sides: \( \ln(y) = \ln((5 + 9x^2)^{\ln(x)}) \)

Step 3 ：Differentiate both sides with respect to \( x \): \( \frac{dy}{dx} = \frac{18x\ln(x)}{5+9x^2} + \frac{\ln(5+9x^2)}{x} \)

Step 4 ：Solve for \( \frac{dy}{dx} \): \( \frac{dy}{dx} = (5+9x^2)^{\ln(x)}\left(\frac{18x\ln(x)}{5+9x^2} + \frac{\ln(5+9x^2)}{x}\right) \)

Step 5 ：\(\boxed{\frac{dy}{dx} = (5+9x^2)^{\ln(x)}\left(\frac{18x\ln(x)}{5+9x^2} + \frac{\ln(5+9x^2)}{x}\right)}\)