find $\frac{dy}{dx}$ for the indicated function y.\ny = 12^x+e^3\n$\frac{dy}{dx}=square$ (type an exact…

Explanation:

Step1: Recall derivative rules

The derivative of $a^x$ is $a^x\ln(a)$ and the derivative of a constant is 0. Here $a = 12$ and $e^3$ is a constant.

Step2: Differentiate term - by - term

The derivative of $y = 12^x+e^3$ with respect to $x$ is $\frac{d}{dx}(12^x)+\frac{d}{dx}(e^3)$. For $\frac{d}{dx}(12^x)$, using the formula $\frac{d}{dx}(a^x)=a^x\ln(a)$, we get $12^x\ln(12)$. For $\frac{d}{dx}(e^3)$, since $e^3$ is a constant, $\frac{d}{dx}(e^3) = 0$. So $\frac{dy}{dx}=12^x\ln(12)+0$.

Answer:

$12^x\ln(12)$