%% Problem 7

%% Initializations
syms x real     % define x as a real symbolic variable
format compact  % eliminates blank lines in output

%% (a)
a = diff( x^3/(x^2+1) )
simplify(a)

%% (b)
a = diff( sin(sin(sin(x))) )

%% (c)
% Here we take the third derivative:
a = diff( atan(x), 3)
simplify(a)

%% (d)
a = diff( sqrt(1+x^2) )

%% (e)
% Remember to use exp for the exponential function, 
% and log(x) for the natural logarithm.
% Note that y = x^x.
y = exp(x*log(x))
simplify(y)
a = diff( y )
simplify(a)
