Mathematics

You're finding the derivative of a product—the exponential $5^x$ times the logarithm $\ln x$. The key is applying the product rule carefully: differentiate each piece, then combine. Remember that $5^x$ has its own derivative involving $\ln 5$, and $\ln x$ becomes $\frac{1}{x}$. Once you have the general formula for $g'(x)$, plug in $x=1$ to evaluate.

You're finding the derivative of a product—the exponential $5^x$ times the logarithm $\ln x$. The key is applying the product rule carefully: differentiate each piece, then combine. Remember that $5^x$ has its own derivative involving $\ln 5$, and $\ln x$ becomes $\frac{1}{x}$. Once you have the general formula for $g'(x)$, plug in $x=1$ to evaluate.