Question

if $r(x)=log_{5}left(\frac{x^{6}5^{x}}{5x^{2}+5}
ight)$, find $r(x)$. select the correct answer below: $r(x)=\frac{6}{xln5}+1 - \frac{10x}{(5x^{2}+5)ln5}$ $r(x)=\frac{5x^{2}+5}{x^{6}(5)ln5}$ $r(x)=\frac{6}{xln5}+\frac{x5^{x - 1}}{5^{x}ln5}-\frac{10x}{(5x^{2}+5)ln5}$ $r(x)=\frac{6}{x}+1-\frac{10x}{5x^{2}+5}$

Explanation:

Step1: Use log - properties

$r(x)=\log_5(x^6)+\log_5(5^x)-\log_5(5x^2 + 5)$

Step2: Differentiate each term

$r'(x)=\frac{6}{x\ln5}+1-\frac{10x}{(5x^2 + 5)\ln5}$

Answer:

$r'(x)=\frac{6}{x\ln5}+1-\frac{10x}{(5x^2 + 5)\ln5}$