How the differentiation happens of the expression $\ln t=\ln r + \ln h$

Question

when we differentiate the expression $\ln t=\ln r + \ln h$ it becomes $(\Delta t)/t=(\Delta r)/r+(\Delta h)/h$ in this what we are differentiating respect to i understand $y= \log x$ which differentiated with respect to x it becomes $dy/dx=1/x$ so how above differentiation works