If $y = 3^x+e^x+x^x+x^3$, then the value of $\frac{dy}{dx}$ at $x = 3$ is

$e^3+54\log_e 3+54$

The correct answer is Option (2) → $e^3+54\log_e 3+54$

$y=3^x+e^x+x^x+x^3$

$\frac{dy}{dx}=3^x\ln3+e^x+x^x(\ln x+1)+3x^2$

At $x=3$

$\frac{dy}{dx}=3^3\ln3+e^3+3^3(\ln3+1)+3(3^2)$

$=27\ln3+e^3+27(\ln3+1)+27$

$=27\ln3+e^3+27\ln3+27+27$

$=54\ln3+e^3+54$

The value of $\frac{dy}{dx}$ at $x=3$ is $54\ln3+e^3+54$.