Question

hw 14 - derivatives of logs section 2.9: problem 9 (1 point)
differentiate $f(t)=\frac{10 + ln t}{10-ln t}$.
$f(t)=square$
preview my answers check answers
you have attempted this problem 0 times.
this homework set is closed.
email instructor

Explanation:

Step1: Recall quotient - rule

The quotient - rule states that if $y=\frac{u}{v}$, then $y^\prime=\frac{u^\prime v - uv^\prime}{v^{2}}$. Here, $u = 10+\ln t$, $v = 10-\ln t$.

Step2: Find $u^\prime$ and $v^\prime$

The derivative of $\ln t$ is $\frac{1}{t}$, and the derivative of a constant is 0. So, $u^\prime=\frac{1}{t}$ and $v^\prime=-\frac{1}{t}$.

Step3: Apply the quotient - rule

$$
LATEXBLOCK0
$$

Answer:

$\frac{20}{t(10 - \ln t)^{2}}$