Frequent Differentiability Differentiation Questions

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How to understand which variable is a function of which other variable. For eg:- In the formula : h = ut - (1/2)g(t^2) the variable h is a function of t How to make similar interpretations in case of other formulas? Can anyon ...

tan-1(2x+1/(1-4x)) ...

find dy/dx if- y=sin2(cot-1(√(1+x)/√(1-x)) ...

tan-1((√(1+x)-√(1-x))/(√(1+x)+√(1-x))) ...

If f(x+y)=f(x)f(y) for all x and y and f'(0) exists show that f'(x)=f'(x).f'(0) for all x ...