Past exam of the mathematical methods II course of the University of Oxford / 2016 resit / 1 / a

For real $x>0$, use logarithmic differentiation: $\log y=\tan x\log x$. The product rule gives $y^{\prime }/y={\sec }^{2}x\log x+\tan x/x$, henceWork on an interval where $\tan x$ is defined. The positive-base condition makes the variable real power unambiguous.