$1\mathrm{.}1.$ Suppose $f(x)=\sqrt[\phantom{2}]{x-7}ln(x^2-25)$

a$.$ As a review of Calculus $1,$ where is $y=\sqrt[\phantom{2}]{x}$ differentiable? Express your answer as an interval or union of intervals.

b$.$ Where is $f$ differentiable where $f$ is defined above. Express your answer as an interval or union of intervals.

c$.$ For $f$ is defined above, find $f^{\text{'}}(x)$