Question

How do I find the derivative of:
f (t) = 125e^((1/6)*ln(38/25)*t)

Answer 1

\[f(t) = 125e ^{1/6} \times \ln |(38/25)t|\]

Answer 2

Use your product rule to split the function into 2 parts
1)\[f(t)=125e^{1/6}\]

2)\[g(t)=\ln(38/25)t\]

\[f \prime (t)=125/6 \times e^{1/6}\]

\[g \prime (t)=\ln(38/25)+1/t\]

Now work the product rule. By the way, I used log rules to split g(t), then took the derivative.