Differentiate the function. $h(t)=\frac{\ln 6 t}{\ln 12 t}$
A) $\frac{\ln 2}{(\ln 12 t)^{2}}$
B) $\frac{\ln 2}{t(\ln 12 t)^{2}}$
C) $\frac{1}{6 t}-\frac{1}{12 t}$
D) $\frac{\ln 2}{t}$

Question

Quizplus · Accepted Answer

Use the quotient rule: 
$$h'(t)=\frac{(\ln 12t)\left(\frac{1}{t}\right)-(\ln 6t)\left(\frac{1}{t}\right)}{(\ln 12t)^{2}}$$
Simplifying, we get: 
$$h'(t)=\frac{\ln 2}{t(\ln 12t)^{2}}$$

Differentiate the Function h(t)=ln⁡6tln⁡12th(t)=\frac{\ln 6 t}{\ln 12 t}h(t)=ln12tln6t​ A) ln⁡2(ln⁡12t)2\frac{\ln 2}{(\ln 12 t)^{2}}(ln12t)2ln2​

Differentiate the Function $h(t)=\frac{\ln 6 t}{\ln 12 t}$ A) $\frac{\ln 2}{(\ln 12 t)^{2}}$