question 6 of 41 step 1 of 1 determine the derivative of the function $g(x)=lnleft(sqrt5{\frac{x - 5}{x +…
question 6 of 41 step 1 of 1 determine the derivative of the function $g(x)=lnleft(sqrt5{\frac{x - 5}{x + 5}}\right)$. answer 2 points
Answer
Explanation:
Step1: Simplify the function
$g(x)=\frac{1}{5}\ln(\frac{x - 5}{x + 5})=\frac{1}{5}(\ln(x - 5)-\ln(x + 5))$
Step2: Differentiate term - by - term
$g^\prime(x)=\frac{1}{5}(\frac{1}{x - 5}-\frac{1}{x + 5})$
Step3: Combine the fractions
$g^\prime(x)=\frac{1}{5}\times\frac{(x + 5)-(x - 5)}{(x - 5)(x + 5)}=\frac{2}{x^{2}-25}$
Answer:
$\frac{2}{x^{2}-25}$