Essential University Physics: Volume 1 (3rd Edition)

$T = \frac{u_k}{\sqrt{1+\mu_k^2}}$
In order to find the expression for the minimum tension needed, we take the derivative of the equation of the previous problem, which is: $\frac{T}{mg}=\frac{\mu_k}{cos\theta+\mu_ksin\theta}$ Taking the derivative gives the answer: $T = \frac{u_k}{\sqrt{1+\mu_k^2}}$