syms x real % define x as a real symbolic variable format compact % eliminates blank lines in output
a = diff( x^3/(x^2+1) ) simplify(a)
a = 3*x^2/(x^2+1)-2*x^4/(x^2+1)^2 ans = x^2*(x^2+3)/(x^2+1)^2
a = diff( sin(sin(sin(x))) )
a = cos(sin(sin(x)))*cos(sin(x))*cos(x)
Here we take the third derivative:
a = diff( atan(x), 3) simplify(a)
a = 8/(x^2+1)^3*x^2-2/(x^2+1)^2 ans = 2*(3*x^2-1)/(x^2+1)^3
a = diff( sqrt(1+x^2) )
a = 1/(x^2+1)^(1/2)*x
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)
y = exp(x*log(x)) ans = x^x a = (log(x)+1)*exp(x*log(x)) ans = (log(x)+1)*x^x