Final answer to the problem
Step-by-step Solution
Specify the solving method
Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Learn how to solve logarithmic differentiation problems step by step online.
$\frac{d}{dt}\left(\frac{1}{3}\ln\left(\frac{t}{9t+1}\right)\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dt(ln((t/(9t+1))^1/3)). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The derivative of a sum of two or more functions is the sum of the derivatives of each function.